We need answer legal client counseling. Need compute expected ranges. Need be careful. Need produce final answer. Let's parse.

We represent Malik. Need advise:

- Plea custody range before and after eight-month credit.
- Probability of each trial outcome.
- Expected trial custody range using only supplied endpoints and probabilities.
- Expected trial custody range after properly accounting for presentence credit.
- License consequence in each branch.
- Probability of no robbery conviction and probability of no incarceration beyond time already served.
- Risk difference between plea and trial without guarantee.
- Concrete recommendation before 4pm and decision Malik personally.

Need adhere. Let's compute thoroughly.

Rules:

Plea offer: Pleads guilty to robbery, firearm dismissed. Custody range 30 to 42 months. Court must credit Malik's eight months presentence custody. So sentence range before credit 30-42; after credit actual additional time? Need articulate. "must credit Malik's eight months of presentence custody." If sentenced to N months (30-42), credit 8, so remaining custodial time = N - 8 = 22-34 months, assuming no other credits. But careful: If he has already served 8 months. Does "range before and after credit" maybe the "plea custody range" is 30 to 42 months, and with credit the remaining exposure is 22 to 34 months. Need not assume exact. If court imposes 30 months, after credit he has 22 left. If 42, 34 left. There is no distribution within range. Also if sentence less than 8? Not in plea range. For trial lesser theft 12-18, after credit 4-10 months. For trial robbery+firearm 84-108, after credit 76-100 months. Acquittal no sentence; no credit? Actually if acquitted no sentence, credit irrelevant; he has served 8 months pre-trial but outcome no incarceration. Could mention if he is acquitted, he walks but 8 months served cannot be undone; "no sentence" so no suspension. But "no incarceration beyond time already served" maybe for acquittal and likely conviction? Need compute probability of no incarceration beyond time already served: outcomes:
- Acquittal: no further incarceration, after serving 8 months? Actually he remains in custody until trial? At time? He has spent eight months in presentence custody. If convicted, sentence credited. If acquitted, he is released, no additional sentence. "No incarceration beyond time already served" means no additional custody beyond the 8 months already served. Probability of acquittal = 25%. But also if convicted only lesser theft, range 12-18 credited by 8, additional = 4-10 months, so > time served. Robbery = 22-34 or 76-100. So only acquittal gives no additional incarceration beyond served. But question says "probability of no robbery conviction and probability of no incarceration beyond time already served." No robbery conviction = acquittal + lesser theft = 25 + 20 = 45%. No incarceration beyond time served = acquittal = 25? Need consider if sentence imposed at low less than credit? no, because 12-18 after 8 still positive 4-10; so only acquittal. If he gets time served? Under ranges, not. Need perhaps "no incarceration beyond time already served" could include plea? If plea range 30-42 credited 8 yields additional 22-34, so no. Good.

Expected trial custody range "using only supplied endpoints and probabilities": They have outcomes:
Acquittal 0.25 -> 0
Lesser theft 0.20 -> 12-18
Robbery+firc 0.55 -> 84-108

Expected custody? Need multiply probabilities times endpoints for low and high. But how to handle acquittal? Low expected = .25*0 + .20*12 + .55*84 = 0 + 2.4 + 46.2 = 48.6 months. High expected = .25*0 + .20*18 + .55*108 = 0 + 3.6 + 59.4 = 63.0 months. So expected trial custody range = 48.6 to 63.0 months before presentence credit? Rule 9: expected custody stated as range by applying probability to low and high endpoints. This includes the no prison branch. Yes. Could also exclude acquittal? No. Then after credit: subtract 8 months from each expected? Is that proper? Need examine. Since credit applies to any custodial sentence after trial; if acquittal no sentence and no credit? Actually 8 months already served. For expected additional custody beyond time served: Need subtract 8 from endpoints per each branch? Let's compute.

Expected trial custody after properly accounting for presentence credit = ? There are two possible interpretations:
1. Subtract 8 from expected custody range computed including acquittal: 48.6 - 8 = 40.6 to 63 - 8 = 55.0 months. But is that "properly accounting" because credit only applies to sentences, not acquittal. However expected additional custody conditional? Let's derive. For each criminal sentence branch, additional after credit = sentence - 8 (or zero if sentence <=8). Since all sentences >8 for lesser and robbery. Acquittal additional = 0 (he is released, no further sentence) but note he already has served 8; no "credit" needed. Expected additional custody = weighted average of max(sentence - 8, 0) across outcomes. For low sentence endpoints: branch lesser low 12 => additional 4; robbery low 84 => additional 76; acquittal 0. Weighted: .2*4 + .55*76 = 0.8 + 41.8 = 42.6. For high endpoints: lesser 18 => 10; robbery 108 =>100; weighted .2*10 + .55*100 = 2 +55 =57.0. So expected additional after credit = 42.6 to 57.0. But if simply subtract 8 from expected range 48.6-63.0 = 40.6-55.0, which is 2 months lower? Let's check because of acquittal branch in expected range includes 0 for acquittal. Subtract 8 from all outcomes, including acquittal would make acquittal -8 impossible. Proper weighted additional gives 42.6-57.0. The difference is 8 * probability of acquittal? Let's compute: E[S] - E[max(S-8,0)]? Actually E[S] = 48.6-63; subtract 8? E[S] - 8 = 40.6-55.0. For additional custody E[max(S-8,0)] = E[S] - 8*P(sentence) - E[?]. Since for all sentences > 8, max(S-8,0)=S-8 for non-acquittal, 0 for acquittal. E[S] includes S=0 for acquittal. E[max] = E[S] -8*P(conviction) = E[S] - 8*0.75 = E[S] -6. So endpoints 48.6-6 =42.6, 63-6=57. Correct. So after properly accounting, expected additional = 42.6-57 months, not expected total sentence minus credit? Wait "expected trial custody range after properly accounting for presentence credit" perhaps the expected total custodial sentence (sentence imposed) after credit? If a judge imposes sentence N and credits 8, "custody" served after trial? We need phrase: Expected additional custody after credit = 42.6 to 57.0 months. Expected sentence range including credit? Before credit 48.6-63. But credit doesn't alter sentence imposed; it alters time remaining. If they ask "plea custody range before and after credit" and "expected trial custody range after properly accounting for presentence credit," they may mean expected additional incarceration. Need be explicit about definitions.

Could there be another way: Expected total time in custody (including the 8 already served) for trial? We can say total expected time served after trial if convicted = expected sentence + 8? Wait if expected sentence before credit 48.6-63, plus 8 already served = 56.6-71 total time from arrest to end? But because credit reduces remaining, total time served = 8 + additional = 8 + (42.6-57) = 50.6-65 months. But the "expected trial custody" maybe should include already served eight months. Need carefully compute.

Let's define:
- Sentence imposed (custody range) after trial if conviction:
  * Lesser theft: 12-18 months.
  * Robbery + firearm: 84-108 months.
- With 8 months credit, remaining additional time if convicted:
  * Lesser: 4-10 months.
  * Robbery: 76-100 months.
- If acquitted: no sentence; no additional time; he will have served 8 months (cannot be restored under facts).

Expected trial sentence imposed (pre-credit) = 48.6-63 months. Does this include acquittal as zero. This is a "sentence range" but is expectation. It represents average of possible imposed sentences over the probability distribution (acquittal = 0).
Expected additional custody after presentence credit = 42.6-57 months. This is the expected amount still to serve after trial and credit. Total expected time from arrest through sentence = 8 + 42.6 = 50.6 months to 8 + 57 = 65 months. Wait if we instead compute expected total actual time served (including pre-sentence 8) from the branch outcomes: acquittal 8 months; lesser theft: 12-18? Actually total time in custody includes 8 presentence + additional after credit = sentence length (12-18). Robbery total = 84-108. So expected total actual custody = .25*8 + .2*(12-18) + .55*(84-108) = 2 + (2.4-3.6) + (46.2-59.4) = 50.6-65.0. Yes. So the expected total time from the point of arrest to completion is 50.6-65 months, not 56.6? Let's reconcile: Expected sentence imposed (48.6-63) plus 8? Wait sentence imposed already includes credit time? A sentence of 84 months means total custody sentence is 84, of which 8 credited, so total time served = 84. So expected total = expected imposed sentence? If acquittal sentence =0 but actual time served =8, so expected total = expected sentence + 8*prob acquittal? Let's compute:
E[S_imposed] = with acquittal=0 = .2*12-18 + .55*84-108 = 48.6-63.
E[total actual] = .25*8 + .2*(12-18)+.55*(84-108) = E[S_imposed] + .25*8 = 50.6-65. So yes. Expected total actual = 50.6-65. Expected remaining after credit = E[total actual] - 8? Because all branches, including acquittal, served 8; if acquitted, after credit? no. Actually expected remaining after credit = E[max(S-8,0)] = 42.6-57. E[total actual] = 8 + expected remaining? For all branches yes because in every branch he has served 8 and, if convicted, additional S-8; if acquitted, additional 0. Thus total actual = 8 + additional. Expected additional = E[total] - 8 = (50.6-65) - 8 = 42.6-57. Good. We can mention both.

Need "Probability of each trial outcome" = 25% acquittal, 20% lesser theft, 55% robbery+firearm. Good.

"Probability of no robbery conviction" = acquittal or lesser theft = 45%; "probability of no incarceration beyond time already served" = only acquittal because lesser theft still adds 4-10 months under range = 25%. But need phrase "assuming a sentence at the low end? Wait no distribution; for no incarceration beyond time served, lesser theft range is 12-18 with credit 4-10. It is impossible under supplied range to have no additional time. So only acquittal." Good.

"License consequence in each branch": Under Harrow, robbery plea or robbery conviction suspends security-officer license for three years after release. Lesser-theft conviction suspends for six months. Acquittal no suspension. Important: The offer is a robbery plea; so if he accepts, license suspended for 3 years after release. If trial and robbery conviction, same 3 years. If trial and lesser theft, 6 months. If acquitted, no suspension. Need mention firearm dismissal? The offer dismisses firearm count; if trial, firearm count adds to robbery. But license consequences tied to robbery conviction/plea and lesser theft. Does firearm count have independent license consequence? Facts say "A robbery plea or robbery conviction suspends... A lesser-theft conviction suspends..." It doesn't mention firearm count. So no separate license consequence. Need maybe mention he cannot work as security officer while in custody anyway; suspension begins after release? Rule says "for three years after release." So if sentenced to custody, license suspension begins after release, extending impact. Need explain branch:
- Plea to robbery: suspension 3 years after release; because sentence 30-42, credit 8 => release after 22-34 additional months, then 36 months suspension, so license unavailable for total ~58-70 months from now? Need calculate. But assignment asks license consequence in each branch, not total loss of license. But maybe helpful. Need not overcomplicate? Let's think.

For plea: If released after 22-34 months, then suspension 3 years. Total period from now without license = 22-34 +36 =58-70 months (4.8-5.8 years), assuming no time off. For robbery conviction at trial: 76-100 additional +36 =112-136 months (9.3-11.3 years) no license. Lesser theft: 4-10 additional +6=10-16 months no license. Acquittal no suspension, but he has been in custody 8 months? "license consequence in each branch" likely only suspension: no suspension. Maybe mention if he is acquitted he can resume licensed work immediately after release, subject to license status not otherwise affected. If "after release" from presentence custody? Acquittal no suspension.

Need maybe include loss of license during sentence? He can't work as security officer while in prison. But "license consequence" defined as suspension after release. In "concrete recommendation," need weigh. Need maybe compare plea vs trial and risk. Need no guarantee. Need "final choice belongs to Malik." Need maybe not authorized to accept. Need present "real numbers" but not invent odds. Need explain expected-value analysis informs but does not compel; risk tolerance matters.

Need compute expected trial outcomes and ranges exactly. Let's organize.

Let's map possible material outcomes:

Option A: Accept plea by 4:00 p.m.
- Conviction: robbery.
- Firearm count dismissed.
- Custody sentence: 30 to 42 months (no distribution; we can't predict point).
- Credit 8 months: remaining custody = 22 to 34 months from today (assuming sentencing today? Offer expires today; if sentenced? We can say "after credit, he would have 22-34 months left to serve under the offer.").
- License suspension: 3 years after release. Total without license from today if no other variables: (22-34)+36 = 58-70 months? Let's check if release after additional 22 to 34 months. If the sentence is 30 and credit 8 -> 22 months left; suspension begins after release (i.e., after serving 22 months) lasts 36 months => 58 months from now. If sentence 42 ->34 +36=70 months. Yes.
- Probability of no additional incarceration? 0% under plea? Since robbery sentence after credit positive; if range 30-42 and credit 8 leaves 22-34 months, no chance of no additional. Good.

Option B: Go to trial.
Trial outcomes:
- 25% acquittal: no sentence, no additional custody beyond time served, no license suspension. He will have served 8 months; cannot get those months back.
- 20% lesser theft only: custody 12-18, credit 8 => 4-10 months additional; license suspension 6 months after release; likely total no license from now = (4-10)+6 =10-16 months (if convicted of lesser).
- 55% robbery + firearm: custody 84-108, credit 8 => 76-100 months additional; license suspension 3 years after release; total no license from now = (76-100)+36 =112-136 months (approx 9.3-11.3 years).
Need maybe "probabilities fixed; do not adjust for evidence." He wants "real numbers." We can show expected values:
Expected trial sentence imposed (before credit) = 48.6 to 63 months.
Expected additional custody after credit = 42.6 to 57 months.
Expected total actual custody including 8 months already served = 50.6 to 65 months.
But wait if expected trial sentence imposed "before credit" includes acquittal =0; if we call it "sentence" maybe for lesser/robbery only conditional? We should be precise. Could also compute conditional expected if convicted? Since Malik might ask "if I go to trial, what's likely?" But rules only supplied probabilities and endpoint range, no distribution. Maybe need compute expected trial custody using all outcomes. Could also compute "if convicted at all (75%), conditional expected sentence range" perhaps useful. Does assignment ask "expected trial custody range using only supplied endpoints and probabilities" and "expected trial custody range after properly accounting for presentence credit." Let's compute conditional expected perhaps because "convicted at trial" vs acquittal. But rule 9 says expected custody range using probability to low/high endpoints. That includes acquittal zero. We'll compute. We can also note conditional on conviction, expected sentence =? Let's see if helpful. Conditional on any conviction (prob 75%), the probability distribution conditional:
- Lesser theft 20/75 = 26.6667%; robbery 55/75 = 73.3333%. Conditional expected low = (0.2*12 +0.55*84)/0.75? Actually E[S_imposed | conviction] = (0.2*12 +0.55*84)/0.75 = (2.4+46.2)/0.75=48.6/0.75=64.8 months. High = (3.6+59.4)/0.75=63/0.75=84.0 months. Conditional expected additional after credit? For convicted outcomes, with credit: expected additional = weighted among convicted = (.2*4 + .55*76)/.75 = (0.8+41.8)/.75=56.8; high =(.2*10+.55*100)/.75=(2+55)/.75=76.0. But assignment might not want conditional. But Malik "trial is basically coin flip" maybe explain 45% no robbery, 55% robbery. The expected range unconditional is more relevant to decision? Maybe include both to avoid ambiguity. However rule 8 says no distribution within range; expected custody must be stated as range by applying probability to low and high endpoints. We can include not conditional unless clear. But answer should not "invent different odds" - conditional probabilities are derived from given, not invented, but might not be necessary. We can perhaps present additional "if convicted" as "for context only" because expected range perhaps hard.

Need be careful: "The probability of no robbery conviction" = 45%. "Probability of no incarceration beyond time already served" = 25% (acquittal) under trial. Could there be a chance under lesser theft that after credit no additional? No because range 12-18 > 8. Under plea? No. So yes.

Need "risk difference between plea and trial without converting the analysis into a guarantee." Need explain:
- Plea gives certainty (100% robbery conviction, no chance of acquittal, 100% additional custody 22-34 months, no chance of 76-100, no chance of lesser 4-10, 3-year license suspension after release).
- Trial has gamble: 25% chance no further prison and no suspension; 20% chance lesser theft + 4-10 months + 6-month suspension; 55% chance robbery + firearm + 76-100 months + 3-year suspension.
- Expected additional custody trial = 42.6-57 months, which is higher than plea's 22-34 additional months. The low end expected trial (42.6 months) is still above plea high end (34 months), so based on expected/custody alone, trial has higher expected additional custody than plea by 8.6? Let's compare:
Plea additional = 22-34. Expected trial additional = 42.6-57. Difference:
- Low vs high? Compare expected trial low 42.6 to plea high 34 => trial expected low is 8.6 months higher than the worst? Wait plea high (34) vs expected trial low (42.6): expected trial low is 8.6 months higher. But if comparing expected values:
Trial additional expected range 42.6 to 57. Plea additional range 22 to 34. Because no distribution for plea, can't compare expected exactly. But one can say expected trial additional is at least 8.6 months higher than plea maximum additional? Let's articulate: Under the fixed numbers, the lower end of the expected additional custody at trial (42.6 months) exceeds the upper end of the plea additional range (34 months) by 8.6 months. However, this does not guarantee Malik will serve more if trial; actual trial outcomes vary: 25% chance serve none, 20% chance 4-10, 55% chance 76-100. The expected value is not a prediction. The "risk difference" is: plea trades away the 25% chance of no additional prison and 45% chance of no robbery conviction to cap? Actually plea doesn't cap? It guarantees 22-34 rather than facing 76-100. It also ensures 3-year license suspension, no chance of 6-month suspension or no suspension. Let's calculate: Plea's maximum additional 34, trial's robbery branch 100. Trial has chance of much worse. The expected value is higher at trial mostly because 55% robbery/firearm with 84-108. Is expected value "higher" in sense of months, yes. Need avoid "expected" meaning likely. The "expected trial custody range" is not the "most likely outcome." The most likely outcome is robbery+firearm (55%) with 76-100 additional after credit. The "expected" is a probability-weighted average, not guarantee. Need maybe mention because Malik says "not what you think sounds safe" - don't use "safe." Provide actual possible outcomes.

Need maybe compute "plea custody range before and after credit" vs "trial expected after credit" not "before credit." We should include both:
Plea:
- Sentence range: 30-42 months.
- Credit: 8 months.
- Remaining to serve after credit: 22-34 months.
Trial:
- Lessor theft: 12-18 months; credit ->4-10 remaining.
- Robbery + firearm: 84-108; credit ->76-100 remaining.
- Acquittal: no sentence/no remaining.
Expected trial sentence: 48.6-63 months (range as expected value using endpoints, including acquittal at zero). Expected remaining after credit: 42.6-57 months. Total expected time in custody from arrest to release: 50.6-65 months (because 8 months already served). Wait need check: If expected remaining after credit = 42.6-57, adding 8 already served gives 50.6-65. But what about if acquitted? Already served 8, no remaining, total 8; included. Yes.

Need maybe not call "expected trial custody range before credit" "sentence" because if acquitted sentence is 0 and credit not relevant. Let's define "S" as sentence imposed; if acquittal, S=0. For lesser/robbery, S in stated range. Then E[S]=48.6-63. After credit, remaining custody after sentencing = max(S-8,0); if acquittal, 0. E[max(S-8,0)] = 42.6-57. But if acquitted, no sentence to credit; he would simply be released. This precise.

Need "expected trial custody range after properly accounting for presentence credit" maybe not "remaining" but "custody range" after credit. Let's maybe display formula:
E[remaining custody after trial] =
0.25×0
+0.20×(12 to 18 − 8)
+0.55×(84 to 108 − 8)
= 0.20×(4 to 10) +0.55×(76 to 100)
= (0.8+41.8) to (2+55)
= 42.6 to 57 months.
This formula already handles the fact that acquittal gets no credit and no sentence. Good. Also "total actual expected custody" = 8 + 42.6 to 57 = 50.6 to 65.

Need maybe compute "expected trial custody range using only supplied endpoints and probabilities" as:
0.25×0 +0.20×(12-18) +0.55×(84-108)
= (0+2.4+46.2) to (0+3.6+59.4)
=48.6 to 63.0 months.
But "before credit." Then after credit = as above. Wait after credit we didn't subtract 8 from expected sentence directly. Need explain.

Need consider "The supplied probabilities already account for evidence. Do not add or subtract probability for those facts." We should state we are not adjusting for witness etc. The probabilities are fixed. "I am not relying on facts to change them."

Need "Counsel must communicate every formal plea offer and advise material sentencing, trial, collateral consequences. Final choice belongs to defendant." We can mention offer deadline and no acceptance by attorney. Since Malik competent and has not authorized counsel to accept. Need advise.

Need "The court may reject a sentencing recommendation but must sentence within applicable range." The prosecutor recommends 30 months but judge can impose 30-42. We should say: Even though prosecution recommends 30, do not treat 30 as guaranteed; no distribution within range, so plea exposure is 30-42, i.e. 22-34 months after credit. We don't know actual sentence; expected range? The rule says don't use midpoint as predicted. For plea, no distribution, so "plea custody range" not expected. We can mention no "expected" value for plea; it is a range.

Need maybe "the court must credit Malik's eight months of presentence custody." If the court imposes 30 months, "remaining" 22 months; if 42, 34. Does "must credit" mean total jail time = 38-50? Some jurisdictions "credit" means sentence max reduced by time served. Yes. We'll state.

Need maybe "after trial, credit is applied to any custodial sentence; no credit applied to acquittal because no sentence." So if convicted lesser after 8 months, he still has 4-10 months more. Need mention.

Need license "security-officer license is principal livelihood." If plea robbery, license suspended after release for 3 years. This may be devastating; if trial robbery conviction, same. If trial lesser theft, only six months after release. If acquitted, none. But note if trial, he cannot receive lesser theft unless jury rejects robbery and firearm? The probability is 20%. Because if convicted only of lesser theft, no robbery conviction. License suspension 6 months after release. Good.

Need maybe "collateral consequences" no immigration/fine/fee. The only collateral consequence specified is license. Need mention no additional charges/mandatory fine/immigration/ fee shifting.

Need perhaps "Probability of no robbery conviction" includes accepting? no. If accept plea, he is convicted of robbery: 0%. At trial: 45% (25+20). Good.

Need "The probability of each trial outcome" in a clear table.

Let's create tables.

Table 1: Plea vs trial possible outcomes.

Plea:
- Conviction offense: robbery (firearm dismissed)
- Probability: if pleads, 100% (offer accepted)
- Sentence before credit: 30-42 months
- Remaining after 8 months credit: 22-34 months
- License suspension after release: 3 years
- Probability of no additional prison: 0 (because 22-34 >0)
Maybe "No robbery conviction" 0.

Trial:
- Acquittal: 25%; sentence 0; remaining 0; suspension none; no robbery conviction yes.
- Lesser theft: 20%; 12-18; remaining 4-10; suspension 6 months; no robbery conviction yes.
- Robbery+firearm: 55%; 84-108; remaining 76-100; suspension 3 years; no robbery conviction no.

Need maybe use "no incarceration beyond time already served": trial 25%; plea 0%. If there is presentence credit, "no incarceration beyond time served" = "would be released" only acquittal. In the lesser branch, 4-10 months further because sentence range 12-18 minus 8. In robbery branch, 76-100 further.

Need maybe "expected trial custody range" and "expected additional after credit" table:
- Expected trial sentence (S, acquittal =0): 48.6-63.0 months.
- Expected remaining custody after 8-month credit: 42.6-57.0 months.
- Expected total actual time in custody (8 + remaining): 50.6-65.0 months.
Maybe "The expected trial sentence is not a possible sentence; it is a weighted-average range." Good.

Let's verify all arithmetic carefully.

Let's compute with exact decimals:
0.20*12 = 2.4; 0.55*84 = 46.2; sum 48.6. 0.20*18 = 3.6; 0.55*108 = 59.4; sum 63.0.
After credit:
Lesser: 12-8=4; 18-8=10. Weighted 0.2:
 low 0.8; high 2.0.
Robbery: 84-8=76; 108-8=100. Weighted 0.55:
 low 41.8; high 55.0.
Acq 0. Sum low 42.6; high 57.0.
Total actual: add 8: 50.6; 65.0. Alternatively expected sentence plus 8*prob acquittal? 48.6+2=50.6; 63+2=65. Because .25*8=2. Good.
Potential issue: We subtracted 8 from both low and high endpoints in robbery and lesser. But if the range is 12-18, credit 8 => 4-10. That's correct. If sentence at 12 exactly, after credit 4. Great.

Need "expected trial custody range after properly accounting for presentence credit" maybe should subtract 8 months from "expected trial custody range" but if we subtract 8 from expected sentence range 48.6-63 to 40.6-55, incorrect? Need decide whether they consider "credit" as applying to expected sentence globally. The assignment specifically says rule 5: "The eight months of presentence custody is credited against any custodial sentence after trial. No credit is applied to an acquittal because no sentence exists." This warns not to simply subtract 8 from all branches. So yes, our "proper" calculation 42.6-57.0 is correct; mention why not just subtract 8 from expected sentence. Need maybe compute both? The assignment asks "expected trial custody range after properly accounting for presentence credit" not "range of expected sentence." We'll explicitly show:
Naively subtracting 8 from expected sentence gives 40.6-55.0, but that would credit the acquittal scenario where no sentence exists. Correct = 42.6-57.0. Is this too much? Could be helpful. But final answer desired overbrevity 5, so not too long, but comprehensive enough. We can include a short note.

Need maybe "plea custody range before and after credit" if accepting plea: before credit 30-42; after credit 22-34. But "plea custody range" maybe "custody range" means the judge must sentence within 30-42; "before credit" range and "after credit" range. Good.

Need "the concrete recommendation before 4 p.m. and the decision Malik must personally make." Need be decisive but not override. Based on numbers:
- The expected additional custody at trial (42.6-57) is worse than plea's guaranteed remaining range (22-34), primarily because 55% chance of robbery+firearm with 76-100 additional and only 25% chance of no additional. Expected value favors pleading. However, the choice depends on risk preferences: if Malik is risk-seeking and values the 25% chance of acquittal and 45% chance of no robbery conviction more than avoiding the 55% chance of 76-100 months and a 3-year license suspension, he might choose trial. As counsel, "I recommend you accept the plea before 4:00 if you cannot bear the 55% chance of a 76- to 100-month additional sentence and the 3-year license suspension. But only you can decide; I cannot accept the offer for you. I will file/not file?" Need "not authorized to accept." Since offer expires 4 p.m. Need perhaps say "You must tell me by 4:00 whether to accept." Do not accept without authorization. The final choice belongs to Malik. Need "concrete recommendation": accept the plea because the trial expected range is materially worse and there is no chance under the plea of the worst 100-month additional or longer license? Wait if accept plea, license 3-year suspension, trial robbery also 3-year suspension but after longer sentence. License difference: plea: after 22-34 months +3 years = 58-70 months without license. Trial robbery: after 76-100 +3 years = 112-136 months without license. Trial lesser: after 4-10+6 months=10-16 months without license. Acquittal: no suspension. Risk. Expected value favors plea because no chance of >34 additional, but guaranteed 22-34 additional and 3-year suspension; trial's upside is 25% no additional/no suspension and 20% shorter prison and shorter license suspension. Let's quantify: Probability of trial doing better than plea on custody? We need compare actual trial outcomes to plea range 22-34 additional.
- Acquittal (25%): better than plea (0 <22-34).
- Lesser theft (20%): 4-10 additional, better than plea.
- Robbery (55%): 76-100 additional, worse than plea.
Thus probability trial outcome would be no worse (actually better) on additional custody than plea: 45% (25+20) if lesser theft all below 22? Yes, lesser high 10 <22. Probability worse than plea: 55% by a lot (76-100 vs 22-34). This is a key risk difference. However, if robber branch lower 76 > plea high 34, yes. So trial has 45% chance to beat plea and 55% chance to be much worse. This might be more intuitive than expected values. Need include.

License comparison:
- Trial acquittal: no suspension (better than plea 3-year).
- Trial lesser: 6 months after release (shorter than plea 3-year) but still a conviction; prison 4-10. Better than plea on prison and license, but it is still a theft conviction; does it affect security license? six-month suspension. No robbery conviction. Maybe from livelihood perspective, 6-month suspension, but less severe than plea. 
- Trial robbery: 3-year suspension after ~76-100 months, but if convicted after trial, release later; total no-license period 112-136 months, much worse than plea. The license suspension "for three years after release": when release is delayed, loss extends. So trial's 55% branch is much worse on license too. But if comparing "suspension period" rather than total time without license, plea and trial robbery both 3 years; however the practical loss of livelihood until release plus suspension is far longer with trial robbery. Need mention.

Need maybe "No incarceration beyond time already served" probability 25%, but "no robbery conviction" 45%. The "lesser theft" outcome still has a six-month license suspension and additional prison, but no robbery conviction and no gun conviction. It's not an acquittal.

Need perhaps "firearm count dismissal" on plea: this avoids a conviction for possession of a firearm during the robbery. Is that a material trial consequence? The charge is dismissed, but the robbery plea counts for license suspension. The firearm count has no separate sentence range? Rule 4: If convicted at trial of both charged counts, aggregate range 84-108. If convicted only of lesser theft, range 12-18. So yes, plea avoids firearm conviction and its potential impact? But not specified license consequence; maybe "possession of a firearm during the robbery" count is dismissed. Need mention: Accepting offer eliminates risk of conviction on firearm count; trial risk is 55% of both counts with aggregate 84-108. If convicted only of lesser theft, the firearm count presumably not proven; no sentence for firearm. But license consequences only as stated. We can note "the robbery plea/firearm dismissal is included in 30-42 range."

Need maybe "The court may reject prosecutor's recommendation" = if prosecutor recommends 30 months, judge might impose 30, up to 42. We shouldn't assume "where a judge will sentence within stated range." In advice, do not treat "prosecutor will recommend 30" as expected. Say "the recommendation is 30, but your exposure is 30-42; treat as range." For comparison, to compare plea to trial expected ranges, use plea range endpoints; no distribution. We cannot say "likely 30" or "expected 36." Need maybe "I cannot give you a point estimate for judge; the rules require range because no distribution." Malik asks "tell me real numbers, not what you think sounds safe." We reply with ranges.

Need maybe "If a sentencing range has no supplied distribution, expected custody must be stated as range by applying probability to low and high endpoints. Do not use midpoint as though predicted sentence." So for trial expected, we have distribution over outcomes but not within each range. We should not use midpoint. Our expected range is exactly that. For plea, no outcome distribution; perhaps "plea custody range" not "expected." For trial, expected range is broad. Good.

Let's think if "expected trial custody range" using only supplied endpoints and probabilities: Should the acquittal probability apply to both endpoints? The range from low to high endpoints is 48.6-63.0. But "expected custody" mathematically with uncertain sentence range should perhaps be interval [E(low), E(high)] if each branch's sentence is unknown but correlated? The rule says state range applying probability to low/high endpoints. We comply. We might say "This is not a possible sentence; it is a range of expected values due to the unstated within-range sentences." Good.

Need maybe calculate "probability of no incarceration beyond time already served" with "lesser theft" might include if sentenced to 8 months? But range 12-18, no. Could there be "time already served" 8 months plus good time? No facts. Not considered. Need not.

Need maybe "no additional charge, mandatory fine, immigration consequence, or fee shifting" in advice? Could mention "There are no other specified collateral consequences; the only one is license suspension." The assignment asks "collateral consequence" in each branch. We'll note.

Potential issue: "Counsel must communicate every formal plea offer and advise the defendant of material sentencing, trial, and collateral consequences." We should maybe explicitly say "This memo/advice communicates the offer and consequences." The answer should maybe be framed as direct to Malik. Use "you" maybe. The user asks "Counsel Malik on..." We can answer as if advising Malik. Need not be too formal but direct. Use "Malik" maybe.

Need maybe "The final choice belongs to the defendant" and "has not authorized counsel to accept the offer." We should not decide for him; but the assignment asks "concrete recommendation" and "decision Malik must personally make." We'll say "I recommend you accept this plea, but I cannot and will not accept it for you; you must tell me by 4 p.m."

Need maybe "before 4pm" if Malik wants to accept, "I need your explicit decision/authorization before 4:00; if you do not, offer expires and the case proceeds to trial with 25/20/55 odds." Since he's in custody maybe "we can communicate by..." not relevant.

Let's examine possible "security-officer license suspension" in plea branch: if sentence 30-42 and "must credit 8 months presentence custody," is "after release" maybe release after 22-34 months. But if he has already served 8 months before plea, is he "released" after sentencing? A presentence custody credit counts toward sentence, so he has already served part of his sentence. The suspension begins after "release" meaning after he completes the full 30-42 months sentence, which is 22-34 months from now. That is correct. If court imposes 30 months with 8 credit, release after 22 months, then suspension begins. Good.

Need maybe "robbery plea or robbery conviction suspends license for three years after release. A lesser-theft conviction suspends for six months. An acquittal produces no suspension." We need "if Malik enters plea to robbery, his security-officer license is suspended for three years after release"—not optional. This is a material collateral consequence. "Firearm count dismissed" no additional license consequence specified. Great.

Need perhaps "If Malik is convicted at trial of both charged counts, applicable aggregate custody range 84 to 108 months." "If convicted only of lesser theft, range 12-18." The probabilities: 55% robbery + firearm, 20% lesser, 25% acquittal. We need maybe not overemphasize "probability of no robbery conviction = 45%" because "lesser theft" is still conviction and additional time. But yes.

Potential nuance: "Plea offer expires at 4 p.m. today. Counsel has supplied complete probability and sentencing record." There is no time to negotiate? Not relevant.

Need perhaps "Expected trial custody range using only supplied endpoints and probabilities" maybe should be "before credit" and "after credit" in one section:
Expected trial custody:
\[
\begin{aligned}
0.25(0)+0.20(12-18)+0.55(84-108) &= 48.6-63.0 \text{ months before credit}\\
0.25(0)+0.20(4-10)+0.55(76-100) &= 42.6-57.0 \text{ months additional after credit}
\end{aligned}
\]
Maybe "total time in custody from now to release? Actually if he remains in custody through trial, he will add more presentence time before sentencing? Wait! This is important.

We need consider timing. The facts: Malik has already spent eight months in custody. Offer expires today. If he goes to trial, trial may occur later; he might remain in custody until trial/sentencing. He will accrue additional presentence time between now and sentencing, which will also be credited? Rule 5 says eight months of presentence custody is credited. But "presentence custody" as of now. If he remains in custody pending trial, he will have more than eight months credit by sentencing. The assignment says "eight months of presentence custody" maybe "supplied complete" and "Malik has already spent eight months in custody." It doesn't mention additional time to trial. Should we account for future additional presentence custody? The governing law says "Under the offer... court must credit Malik's eight months of presentence custody." Rule 5: "The eight months of presentence custody is credited against any custodial sentence after trial. No credit is applied to an acquittal because no sentence exists." It fixed eight months. The assignment likely wants credit exactly 8. We should not add speculative additional time before trial. But if trial occurs later, he would have more time served. However, no duration to trial is supplied; cannot invent. Use only eight. Maybe if he remains in custody, his credit increases; but not supplied. We can maybe phrase "based on the eight months supplied; if additional presentence time accrues before sentencing, that would be credited too, but no duration is provided and I cannot estimate it." But the rule says supplied complete record; maybe not invent. Should I mention? Since asked "properly accounting for presentence credit" and facts say eight months. I think mention "on the supplied 8 months" to avoid. But not necessary? Maybe in final: "Using the stipulated 8 months of credit; I am not estimating any additional pretrial time." Good.

Need maybe "If Malik is acquitted, he serves 8 months and is released. Time already served cannot be restored; no sentence, no credit, no suspension." Good.

Let's examine "expected trial custody range after properly accounting for presentence credit" in possible issue: If a person receives a sentence of 84-108 with credit for 8, the "custody range" after credit is 76-100, but if they already served 8, perhaps "time served" counts toward the sentence and "additional custody" is 76-100. But if the 8 months were served before trial, and trial occurs after today, there is still time between now and trial; no credit beyond 8. We don't know. Fine.

Need maybe "risk difference" includes "plea custody range after credit (22-34) vs trial's expected additional (42.6-57)"? Actually compare plea range to expected trial range:
- Plea guaranteed 22-34 additional.
- Trial expected additional 42.6-57, which is materially higher. But because expected range includes 55% high branch and 25% zero, some clients may prefer trial. We can say "If you value avoiding the worst outcome, the plea eliminates the 55% chance of 76-100 additional. If you value the chance of walking/lesser, trial offers 45% chance no robbery conviction and 25% chance no further prison." Need maybe "The trial is not 'basically a coin flip' in the way you said? Let's examine. The probability of no robbery conviction is 45%; probability of robbery conviction is 55%. That is close to a coin flip regarding robbery conviction. But regarding additional prison beyond time served, only 25% chance of no additional prison and 55% chance of very long prison. So it's not a coin flip between no prison and 9 years; it is 25/55/20." This is important because Malik says "I will not plead if trial is basically a coin flip, but I cannot do nine years." Need address. The odds:
- Robbery conviction: 55%, not 50, but yes near coin flip. However, the "coin flip" branch if he loses is not 9 years exactly: if the robbery+firearm branch occurs, sentence 84-108, additional after credit 76-100; if he "wins" no robbery, he still has 20% chance of lesser theft with 4-10 additional, and 25% chance no additional. So not just coin flip between 0 and 9 years. Actually "cannot do nine years"—under trial, if he loses robbery, the potential sentence is 84-108, which is 7-9 years, after credit remaining 76-100 months = 6.33-8.33 years; the high end is 9 years sentence (before credit) and 8.33 years after credit? Wait let's compute:
84 months =7 years; 108 months=9 years. After 8 credit, 76 months=6.33 years; 100 months=8.33 years. If asking "cannot do nine years" maybe if sentence at 108, total sentence 9 years, but with credit actual additional 100 months (8 years 4 months). Total time from arrest to release =108 months =9 years. He said cannot do nine years; 108 is highest. There is 55% chance of a robbery conviction, and if so the sentence range is 84-108 before credit. The court could impose 9 years (108); no distribution. Cannot guarantee not 9 years. Thus if he truly cannot do 9 years, the plea avoids that risk? Under plea, max 42 months sentence =3.5 years, additional after credit 34 months =2.83 years; total from arrest to release =50 months =4.17 years? Wait if sentence 42 + 8 credit? Total actual time =42 months, not 50? Let's think. If he has served 8 months, the 42-month sentence includes that time? Yes total sentence 42 months from date of sentencing? Actually jail credit means time served counts toward sentence. If sentenced to 42 months and credited 8, release after 34 additional months after sentencing. Total time from arrest to release =8+34=42 months. If sentence 42, total actual custody =42 months =3.5 years. The phrase "after credit 22-34 months" is additional from now; total from arrest to release =30-42 months, i.e., 2.5-3.5 years. Wait check if now = after 8 months served. If sentenced 30, credited 8, release after 22 months; total from arrest to release =30 months. Yes. So "plea total from arrest to release" = 30-42 months, not 30? Actually total actual time = sentence length because credit counts. So if sentence 42, total =42 months. Good. For trial robbery, total actual time =84-108 months because credit counts. "Additional after credit" =76-100. Total from arrest =84-108. So "cannot do nine years" means cannot risk 108-month sentence. Plea max total from arrest =42 months, much less. Good. Need maybe not confuse.

Let's compute "plea after credit" maybe "remaining additional from now" 22-34; if comparing to "cannot do 9 years," use sentence range/total not additional. "Under plea the maximum sentence is 42 months (total, with credit), so you would be released no later than 3.5 years after arrest; after today's 8 months that is 34 more months. Trial robbery branch exposes you to a total sentence of 84-108 months (7-9 years)." Wait if he already served 8, total after release =84-108; additional 76-100. Yes.

Need maybe "if trial and convicted only lesser theft, total sentence 12-18, additional 4-10; total from arrest =12-18. If acquitted, total =8 months (served) no sentence." Good.

Need think if "credit" in plea: "The court must credit Malik's eight months of presentence custody." If court imposes 30-42, after credit "remaining" 22-34. But if we say "total from arrest to release =30-42" maybe that's a more intuitive way. We can include both:
Plea:
- Sentence: 30-42 months total.
- Eight months credited; remaining to serve: 22-34 months.
Thus he is not exposed to anything near 9 years under plea.

Trial:
- Robbery conviction: sentence 84-108 total; 8 credit; remaining 76-100.
- Lesser theft: sentence 12-18 total; remaining 4-10.
- Acquittal: 0 sentence; released (after 8 months served).
Expected total from arrest: 50.6-65 months; expected remaining after credit: 42.6-57.
Need maybe "expected total from arrest" perhaps includes current 8 months; if Malik asks "real numbers" we can give. But the assignment specifically doesn't ask "expected total from arrest." It asks "expected trial custody range after properly accounting for presentence credit." I'll include total maybe as part of clarity.

Potential issue: The "applicable custody range" for trial if convicted of both charged counts is "aggregate custody range 84 to 108 months." Does "credit" reduce the sentence below the minimum? Wait if court imposes 84 months and credit 8, does that mean he is sentenced to 84 and released after 76, but if total time from arrest =84. Correct. No issue.

Need maybe "No probability supplied for sentence at any particular point within a range" — so our expected range is not "point estimate." Need mention "I cannot tell you 'real numbers' as a single point. The only honest number is the range and probabilities." This addresses Malik's "real numbers, not what you think sounds safe." We can say "The rules and record do not allow me to pick a point. A single 'expected number' would be invented. Here's the range."

Let's maybe draft final in sections:

1. "The offer and credit"
- Formal offer: Plead guilty to robbery; firearm count dismissed; sentence range 30-42 months; prosecutor recommends 30 but judge can impose up to 42.
- Credit: 8 months, so additional custody after sentencing: 22-34 months. Total sentence from arrest: 30-42 months. License: 3-year suspension after release.

2. "Trial branches"
Table:

| Outcome | Prob | Sentence | Remaining after 8-mo credit | License |
| Acquittal | 25% | 0 | 0 | none |
| Lesser theft | 20% | 12-18 | 4-10 | 6 months after release |
| Robbery+firearm | 55% | 84-108 | 76-100 | 3 years after release |

Maybe "Remaining after credit" if acquittal no credit but no sentence; "0 additional" yes.

3. "Expected trial numbers"
- Expected trial sentence (before credit): 48.6-63 months.
- Expected additional custody after credit: 42.6-57 months.
- Expected total actual custody (including 8 served): 50.6-65 months.
Maybe formula:
Before credit: 0.25(0)+0.20(12-18)+0.55(84-108) = 48.6-63.
After credit: 0.25(0)+0.20(4-10)+0.55(76-100)=42.6-57.
Use "This is not a possible sentence; expected range only."

4. "Probabilities no robbery/no more time"
- No robbery conviction: acquittal + lesser theft =25+20=45%.
- No incarceration beyond time already served: only acquittal =25%. Because lesser theft still leaves 4-10 after credit; robbery leaves 76-100; plea leaves 22-34. Wait plea has no probability "no incarceration"; for trial, only acquittal. Good.

Need maybe "The probability of robbery conviction is 55%, so in that sense it's slightly more likely than a coin flip. But there is a 45% chance the robbery count is not proven. If the robbery count fails, there is still a 20% chance of lesser theft with 4-10 additional months and a six-month suspension; 25% chance acquittal with no further custody or suspension."

5. "Risk difference"
- Plea: certain robbery conviction; certain 22-34 additional; certain 3-year suspension. No chance of acquittal/lesser; no chance of 76-100. 
- Trial: 45% chance of no robbery conviction; 25% chance no further prison; 20% chance shorter prison and shorter suspension; 55% chance much worse: 76-100 additional and 3-year suspension after a much later release. 
- Expected-value comparison: Expected additional at trial is 42.6-57 months, which is higher than the plea's 22-34 months. The low end of expected trial additional (42.6) is 8.6 months above the plea's high end (34)? Need phrase carefully: "By these fixed numbers, the trial's expected additional-custody range is above the plea's range: even the lower bound of the expected trial number (42.6 months) is higher than the maximum additional custody under the plea (34 months)." This is true but maybe weird because expected trial lower vs plea high. It means expected value strongly disfavors trial. We can say "Expected-value analysis points toward plea, but it doesn't decide it." 
- "No guarantee": A trial could produce 0 additional custody with 25% chance, or 4-10 with 20% chance. If Malik cannot tolerate the 55% chance of 76-100 additional and 3-year suspension after a much later release, plea is safer/less punitive. But if he is willing to risk it for chance of acquittal, trial is rational. Need not "convert into guarantee."

6. "Recommendation and decision"
- "My concrete recommendation: accept the plea by 4 p.m." Maybe phrase "if the deadline cannot be extended and you want to avoid the realistic possibility of 84-108 months, yes, I recommend accepting." But because final choice is his; "you must personally decide and authorize me to accept before 4. I will not accept without your instruction."
Need maybe "If you choose trial, we prepare; but the offer will be gone." Good.

Need maybe "If you plead, the firearm count is dismissed and no additional charges/fines/immigration/fees; but you will have a robbery conviction and 3-year license suspension." Good.

Need perhaps "No probability is supplied for a sentence at any particular point within a range, so I cannot tell you whether the judge will sentence at 30 vs 42. The prosecutor will recommend 30, but the court could reject it and go up to 42. You must assume 30-42." This is important. We'll include.

Need maybe "License consequence in each branch" use "after release": For plea, release after 22-34 months; then 3-year suspension. For trial lesser, release after 4-10 months; then 6-month suspension. For trial robbery, release after 76-100 months; then 3-year suspension. For acquittal, no suspension. We can also include "total time without license from now" if useful:
- Plea: 58-70 months.
- Trial lesser: 10-16 months.
- Trial robbery: 112-136 months.
- Acquittal: 0 months suspension (though currently in custody; once released can resume if license unaffected). Are those numbers correct? Let's calculate total time without license from now through suspension:
Plea: 22-34 additional + 36 = 58-70.
Trial lesser: 4-10 + 6 = 10-16.
Trial robbery: 76-100 + 36 = 112-136.
Acquittal: 0 + 0 = 0? If he's been in custody for 8 months, he hasn't been working as security officer; but the license isn't suspended. The "license consequence" is no suspension. If asked "license consequence" not "time without license" maybe no need. But maybe we can add a parenthetical "Because the suspension runs after release, a longer prison sentence also delays the start and lengthens the practical loss of the license." Maybe not compute total no-license time? It might be helpful but maybe too much? Desired oververbosity 5. But assignment asks "license consequence in each branch"; include after release; parenthetical for total maybe okay.

Need maybe "security-officer license is principal livelihood" in recommendation: If he accepts, 3-year suspension after release, not during custody. This is significant but less than a robbery conviction after trial? Wait if trial robbery, also 3-year suspension after release, but because release later, total livelihood loss is much longer. If he gets lesser theft, license suspension is only six months after release. This may be a strategic factor. Need mention.

Need maybe "If Malik is acquitted, he is not convicted of robbery or theft, no license suspension." Good.

Potential issue: Does the driver's testimony "already charged, no written cooperation agreement, hopes for leniency" maybe matter? Rule 8 says supplied probabilities already account for credibility problems; do not adjust. We must not revisit. We can explicitly say "I am not changing the 25/20/55 for the driver or other evidence." Good maybe in final "I am using your counsel's fixed odds; no adjustment based on witness credibility etc. because those are already baked in." But not necessary.

Let's consider whether there are legal ethics duties: "Counsel must communicate every formal plea offer and advise defendant; final choice belongs to defendant." We can mention "This advice does not substitute for your decision. If you reject, we go to trial." Good.

Let's maybe include "You said you will not plead if trial is basically a coin flip, but you cannot do nine years." We can respond:
- It is not "basically a coin flip" between no prison and nine years. It is: 25% acquittal, 20% lesser theft (4-10 additional months), and 55% robbery+firearm (76-100 additional months). The robbery count is slightly more likely than not (55%). If the 55% hits, the sentence range is 7-9 years total (84-108 months), and the judge could sentence at 108. You cannot be guaranteed not to do nine years if you go to trial. The plea caps your total sentence at 42 months (3.5 years), or 22-34 additional after credit. This directly addresses his statement. Need include perhaps.

Let's ensure "cannot do nine years" in terms of "sentence" vs "additional." If trial robbery branch top end 108 months = 9 years. After credit, additional max 100 months = 8 years 4 months. The "sentence" is 9 years, but with credit he spends 8 years 4 additional months. If he says "cannot do nine years" might refer to total from now? Let's clarify:
- If convicted at trial of robbery+firearm, sentence is 84-108 months (7-9 years). Credit reduces remaining time but the sentence itself includes the credit; total time in custody from arrest to release is 84-108 months. So maximum total from arrest is 9 years. If "cannot do nine years" means cannot risk total, plea total max 42 months. If "cannot do nine years" colloquially maybe "additional time" after credit: max additional after credit is 100 months (8 years 4 months). Still close to 9 years. We need avoid misleading. Use "sentence range 84-108 months; with the 8-month credit, that means 76-100 months still to serve after today, and the total time from arrest to release would be 84-108 months." Good.

Need maybe "lesser theft conviction: 12-18 total; with 8 credit, 4-10 additional; total from arrest =12-18." Good.

Let's think if "after trial" includes possibility of additional pre-sentence time beyond 8. We can phrase "Using the stipulated 8 months of credit as of today." Since if he remains in custody during trial, actual credit at sentencing may be higher; but not specified. Hmm, should we perhaps avoid "from today" because by time of trial more time may pass? But the assignment says eight months presentence custody; likely assume for decision. We can say "on the current eight months." Good.

Could there be "probation/supervised release" not specified; no.

Need maybe "The court may reject a sentencing recommendation but must sentence within applicable range" — For plea, if judge rejects 30, can impose up to 42; not below? Applicable custody range 30-42, yes. For trial, ranges. Good.

Need maybe "The firearm count is dismissed" if plea: This means no conviction for firearm count; under plea, no range for firearm. At trial, "both charged counts" aggregate range maybe includes both; no separate "consecutive/concurrent" issue. We'll not speculate.

Let's maybe craft final answer in a coherent memo style:

```
Malik,
This is the plea decision you have to make by 4:00 p.m. I am using the fixed probabilities and ranges; I am not guessing where the judge will sentence.

1. If you accept the offer:
- Conviction: robbery.
- Firearm count: dismissed.
- Sentence range: 30-42 months. The prosecutor will recommend 30, but the judge can go up to 42; there is no supplied distribution within the range.
- After 8 months' credit: 22-34 months more in custody.
- License: suspended for 3 years after release.
- There is no chance of no additional custody if you take the plea.

2. If you go to trial:
...
```

Then tables.

Need maybe "expected trial custody range before/after credit" in table maybe. Let's do.

Potential mathematical notation in final: Since final answer desired oververbosity 5, not too lengthy but enough. But the problem asks multiple items; need ensure all addressed. Use bullets.

Let's think deeper about "expected trial custody range after properly accounting for presentence credit." We computed expected remaining after credit. But could also compute "expected trial custody range after credit" as "expected imposed sentence (48.6-63) minus credit in non-acquittal branches =42.6-57." We should explain why not simply 48.6-63 - 8 =40.6-55. Because the acquittal branch has no sentence. Let's explicitly state:
"Although you might think subtract 8 from the 48.6-63 expected sentence, that would improperly credit the acquittal scenario. Since acquittal is 25%, the correct expected remaining time after credit is 42.6-57." This is advanced but important. Maybe overkill? The assignment likely expects this nuance. Include one sentence.

Need perhaps "probability of no incarceration beyond time already served" maybe "25% (acquittal) in trial; 0% in plea." It says "probability of no robbery conviction and probability of no incarceration beyond time already served" perhaps two separate calculations. We'll state:
- No robbery conviction: at trial 45% (25% acquittal + 20% lesser theft). Under plea, 0% because plea is robbery.
- No incarceration beyond time already served: at trial 25% (only acquittal); under plea 0%.
Need maybe if "lesser theft" is "conviction only for lesser theft" and "theft offense" not robbery, so no "robbery conviction" yes. Good.

Let's examine "acquittal" branch license: "An acquittal produces no suspension." But he will have been in custody eight months; "no incarceration beyond time already served" means he is released, but has no "sentence" and no "credit." Could he get credit for time served before acquittal? No because no sentence; but he's out. Good.

Need "The expected trial custody range using only supplied endpoints and probabilities": maybe if a branch produces "range" we combine. We need perhaps "expected sentence range" not "expected custody range" because "acquittal produces no sentence." But okay.

Let's maybe write "Expected trial sentence, counting acquittal as zero: 48.6-63 months." Maybe "sentence" is odd for acquittal; but good.

Let's think about if "expected trial custody range after properly accounting for presentence credit" perhaps in expected ranges after credit:
- Acquittal: 0
- Lesser theft: 4-10
- Robbery: 76-100
Expected additional = 42.6-57.0. Yes.

Need perhaps "Plea custody range before and after credit" maybe if the judge imposes 30 and prosecutor recommends 30, "after credit 22 months" but if judge imposes 42, "after credit 34." We should not ignore prosecutor's rec. Rule "court may reject recommendation but must sentence within applicable range." The "range" is 30-42; no distribution. We'll say "The recommendation is not a cap; treat the range as 30-42." Good.

Let's perhaps include "The judge cannot sentence below 30 or above 42 on the plea." Good.

Need perhaps "concrete recommendation" maybe:
"Based solely on these numbers and assuming no other nonlegal factors, I recommend pleading. The trial has a 55% chance of a sentence of 84-108 months; the plea gives a guaranteed maximum of 42 months. The expected additional custody after credit is worse at trial (42.6-57) than the plea (22-34). The plea also avoids the risk of a firearm conviction. It does cost you the 25% chance of no further custody and the 20% chance of a lesser-theft outcome and shorter license suspension. If you need me to try to beat the offer? No, it expires. The decision is yours; I cannot accept unless you say so. If you do not accept, we try the case."

Need maybe "The final choice belongs to Malik" maybe in conclusion:
"I am authorized to advise but not to decide. You have not authorized acceptance. If you want the offer, tell me before 4:00. If not, we will go to trial and the offer will be gone." Good.

Need maybe "not converting into a guarantee" in recommendation:
"I am not guaranteeing what a judge would do. If you plead, the judge could still sentence 42. If you go to trial, you might be acquitted. This is risk, not certainty." Good.

Let's think about possible "risk-neutral" expected-value analysis: The assignment says "Expected-value analysis informs advice but does not compel a risk-neutral defendant." We can say "Expected value favors the plea, but you can rationally choose trial if you value the 25% acquittal and 20% lesser-theft chance enough to bear the 55% robbery risk. That's your call." Good.

Potential issue: "Trial is basically a coin flip" maybe because 55/45; we should correct "55% robbery conviction and 45% no robbery conviction; close but not exactly a coin flip. More importantly, the 'no robbery' branch is not a clean win: 20 of the 45 points still mean conviction for theft, additional prison time, and a license suspension. The clean-win branch is only 25%." This is a great point; include.

Let's consider "The Plea Offer Before Dawn" title maybe maybe from problem; no need.

Let's maybe draft final answer as if direct speech to client.

Potential need to "state the probability of each trial outcome" maybe in table: 25%, 20%, 55%. Yes.

Let's also maybe mention "No probability supplied for sentence within any range; I therefore state ranges, not midpoints. No exact 30 vs 42 or 84 vs 108 prediction." At top.

Let's formulate final answer carefully.

Let's ensure no "invent different odds" in final: "I have not adjusted the 25/20/55 based on the driver, video, or DNA." Could include.

Potential "material sentencing, trial, and collateral consequences":
- Sentencing: plea range 30-42; trial lesser 12-18; trial both 84-108; credit.
- Trial: probabilities; no other charges/fees.
- Collateral: license suspension; no immigration/fine/fee. We'll mention "no immigration consequence/fine/fee shifting is specified."

Need maybe "firearm count dismissed" if plea: It's a material trial consequence. In plea table, include "firearm count dismissed." In trial table, include "firearm count at risk; 55% conviction on both counts." Good.

Let's maybe present table with "Trial branch" including "Firearm count?":
- Acquittal: no conviction; firearm not proven.
- Lesser theft only: no robbery/firearm conviction? The firearm count? If convicted only of lesser theft, presumably firearm count not proven; "no robbery conviction." Good.
- Robbery+firearm: both counts.

Maybe "robbery plea" "firearm count dismissed" "license suspension" no mention of firearm license. Good.

Let's maybe compute "total no-license time" optional:
If we include, be careful: "time without license" includes incarceration while he cannot work, but the suspension after release may be additional. If he's in prison, he cannot work as security officer regardless of license. But the "license consequence" is suspension after release; if he is in prison, he's not working anyway. This broader "time without license" could be useful but not asked. It might confuse. Let's not include total no-license time unless in parenthetical. Maybe one sentence:
"Because any prison sentence prevents you from working as a security officer anyway, the practical livelihood difference is not just 3 years vs 6 months; the trial robbery branch's much longer prison term also delays the start of the 3-year suspension." Good but not necessary. Desired oververbosity 5; we can include.

Need maybe "The probability of no robbery conviction" under plea? 0; at trial 45. "Probability of no incarceration beyond time already served" under trial 25. We'll include.

Need maybe "risk difference between plea and trial without converting into guarantee":
Let's phrase:
"Plea removes the 55% bad tail. It also removes the 45% upside. Trial is not a coin flip between 'walk' and 'nine years'; it is 25% walk / 20% lesser / 55% robbery. Accepting the plea means the robbery conviction is certain and the 3-year license suspension is certain. Rejecting it means a 55% chance of all that plus 76-100 months more to serve, a 20% chance of a much shorter sentence and suspension, and a 25% chance of no further prison." This is the risk difference.

Need maybe "The expected trial additional-custody range is 42.6-57, vs plea additional 22-34. Thus, on expected months, trial is worse. But because no distribution within ranges, these are ranges, not certain predictions." Good.

Let's verify "plea additional 22-34 vs trial expected 42.6-57" if comparing expected values, yes:
Plea no distribution, actual sentence unknown within range; expected additional unknown but between 22 and 34? Actually if no distribution, the "expected" additional under plea is some unknown between 22 and 34, not necessarily the whole range. We should not call "expected plea" 22-34? We can say "actual additional custody under the plea will be somewhere in 22-34; because no distribution is supplied, I cannot give a more specific expected value." The trial expected is 42.6-57; if comparing expected under assumptions, if plea expected is between 22 and 34 and trial expected lower 42.6 > plea upper 34, then even under worst expected plea point (34) the trial expected low is higher. But is it valid to compare "expected trial low" to "plea max"? Yes, as a dominance argument regarding expected value, if plea expected max is 34 and trial expected min 42.6. But because trial actual distribution includes better outcomes, expected value is not decisional. We can say "If you minimize expected months, the plea dominates under these fixed numbers." But maybe not overstate "dominates" due to non-custody/license/upside? Actually "dominates" in expected value but not actual stochastic; plea and trial are not comparable by "dominance" because trial has chance of better outcome. The expected value is higher for trial. Use "expected-value analysis favors plea" rather than "dominates."

Need maybe "plea guarantee" not "cap"? The plea "guarantees additional custody between 22 and 34" but the "sentence" might be 30-42; if the judge has discretion and must credit, yes. The actual number still unknown. "Guarantee" no chance of zero? Yes.

Could there be "prosecutor will recommend 30 months" and "judge may reject a sentencing recommendation but must sentence within applicable range" - If plea, if judge rejects the 30 rec, can the defendant withdraw? Rule doesn't say. Do not assume withdrawal. Good.

Need perhaps "defendant has not authorized counsel to accept offer" - we can say "I am not accepting this offer now; the acceptance requires your instruction before 4:00." Good.

Let's think if "the court may reject a sentencing recommendation" in Harrow means if judge rejects 30, he could sentence up to 42. The "plea offer" says "prosecutor will recommend 30" maybe not "specific plea agreement under Rule 11(c)(1)(B)" but "offer" with recommendation. We should not infer he can withdraw if judge rejects. Good.

Potential "firearm count dismissed" on plea: Does this affect "armored pharmacy robbery" sentence? No, within 30-42. Good.

Potential "lesser theft offense" after trial: The facts "If Malik is convicted only of the lesser theft offense"; the jury can convict of lesser included? Probability 20. Good.

Need maybe "acquittal produces no sentence" and "no credit is applied to an acquittal because no sentence exists" - If acquitted, "not incarcerated beyond time already served" but "time already served cannot be undone." We'll say "The 8 months served is a sunk cost; acquittal doesn't 'credit' it, it just means you would be released." Good.

Need maybe "the eight months presentence custody credited against any custodial sentence after trial" — If he goes to trial and receives lesser theft 12-18, the credit reduces remaining to 4-10, but "total sentence" 12-18. Good.

Let's maybe plan final text:

```
Malik,

I’m using only the fixed record. The offer expires at 4:00; if you reject it, it is gone.

THE PLEA
- ...
```

Let's write final answer maybe in "Counsel's advice" form.

Let's ensure final answer includes all assignment items:
- Plea custody range before and after credit: yes.
- Probability of each trial outcome: table.
- Expected trial custody range endpoints/prob: yes.
- Expected trial custody range after credit: yes.
- License consequence in each branch: table.
- Probability no robbery conviction/no incarceration beyond time served: yes.
- Risk difference: yes.
- Concrete recommendation and decision: yes.

Let's maybe include "Expected trial custody range using only supplied endpoints and probabilities" before credit; then "after properly accounting for presentence credit." Table can have expected numbers.

Let's maybe write formulas in final with arithmetic.

Potential issue with "expected trial custody range after properly accounting for presentence credit" if "credit" after trial also applies to "lesser theft" and "robbery" but if acquittal no sentence. We use 0 for acquittal. Good.

Let's maybe include "The expected trial sentence before credit is not the same as expected additional time after credit; subtract 8 only on conviction branches." Good.

Let's perhaps include "If you remain in custody between now and trial, additional presentence time may increase the credit, but the record gives no duration for that, so I do not estimate it." Is that needed? Maybe not. But if I say "from today" and trial may happen later, future pretrial detention would be credited. The assignment didn't provide trial date, so "using supplied 8 months" avoids. Add a footnote-like sentence: "I am using the stipulated eight months already served; any later additional presentence custody would also be credited but no amount is supplied." This is legally accurate but maybe not necessary. The problem says "complete probability and sentencing record below" and "supplied" probabilities; no future duration. We can include at end of credit section.

Let's think if "time already served" = "eight months of presentence custody" before plea; if he accepts plea and sentencing occurs after 4pm today, does he have additional presentence time? If sentence can be imposed today, no. But if plea is accepted and sentencing later, he may accrue more time. The facts maybe assume no additional time. We don't need.

Let's maybe produce with "total from arrest" numbers:
- Plea: 30-42 total (sentence), after credit 22-34. This is because credit counts. Actually "total from arrest to release" equals sentence length if credit is applied and no other factors. If he has already served eight, release occurs when sentence served. So 30-42 total. Good.
- Trial lesser: 12-18 total; after credit 4-10. If acquittal: 8 total served (not sentence). Good.
- Trial robbery: 84-108 total; after credit 76-100. 
This "total from arrest" is a helpful context. We'll include maybe in table columns "Total sentence/with credit" and "additional after credit."

Let's prepare final table:

```
Outcome | Prob | Total custodial sentence | Remaining after 8-month credit | License after release
Plea robbery | 100% (if accepted) | 30-42 months | 22-34 months | 3-year suspension
Trial acquittal | 25% | 0 (no sentence; 8 months served) | 0 additional | none
Trial lesser theft | 20% | 12-18 months | 4-10 months | 6-month suspension
Trial robbery + firearm | 55% | 84-108 months | 76-100 months | 3-year suspension
```

Need maybe "Total custodial sentence" for acquittal not "sentence" but "custody served =8." Table says "0 (no sentence)" maybe okay. Maybe "No sentence; would be released (after 8 months already served)" to avoid "0 total custodial" because he served 8. Let's not confuse:
Columns:
- Trial outcome | Probability | Sentence imposed | Additional time after credit | License.
For acquittal: sentence imposed "none"; additional "0" (released); license "none".
For plea: sentence imposed "30-42"; additional "22-34"; license "3 years after release".

Then in expected after credit, "additional time" is relevant. If "total actual time including 8 months" for acquittal is 8, okay.

Need maybe "Plea robbery" probability 100? If he accepts; yes. But probability of each trial outcome only for trial. We can table trial only.

Let's maybe include "Firearm count" in table:
Plea: firearm dismissed.
Trial robbery+firearm: both counts, sentence 84-108.
Trial lesser theft: no robbery conviction; firearm count not proven? maybe not include.

Let's maybe write:

```
Trial branch table:
- Acquittal (25%): Firearm count not proven. No sentence. No more time (but 8 months already served). No license suspension.
- Lesser theft only (20%): No robbery conviction. Sentence 12-18; after 8 months credit 4-10 more. License suspended 6 months after release.
- Robbery + firearm (55%): Convicted of both. Sentence 84-108; after credit 76-100 more. License suspended 3 years after release.
```

Good.

Need maybe "Expected trial numbers" table:
```
Expected sentence imposed (acquittal = 0): 48.6-63 months.
Expected additional custody after credit: 42.6-57 months.
Expected total time in custody from arrest (8 + additional): 50.6-65 months.
```
Will "expected total time from arrest" maybe for acquittal has 8 months served; for sentence branches includes current 8. Add "These are weighted averages, not possible actual sentences." Good.

Need maybe "No robbery/no more time" after expected:
```
No robbery conviction at trial: 20+25 =45%.
No additional incarceration beyond the eight months already served: 25% (acquittal only).
Under the plea: no robbery conviction 0%; no additional incarceration 0%.
```
Actually "under the plea no additional incarceration 0%" because additional 22-34 >0; yes. Could be odd to say 0%? There is no probability range; plea outcome certain. Maybe "not available." We'll state.

Need maybe "Risk difference" with "no guarantee":
```
Plea: No chance of acquittal; no chance of 4-10; no chance of 76-100. You give up 45% no-robbery and 25% no-further-prison. In exchange, you get a certain max 42-month total custody and no firearm conviction.
Trial: 55% chance of 84-108 sentence; 45% chance no robbery; 25% chance no further prison. Expected months favor plea. But there is no guarantee; 45% chance you would be glad you rejected the plea, 55% chance you would not be.
```
Need perhaps "max 42-month total custody" under plea because if sentence 42; "after credit, 34 additional" but total from arrest 42. Good.

Need maybe "concrete recommendation before 4":
```
I recommend accepting the offer if you cannot accept the 55% risk of a 84-108-month sentence. But I cannot decide for you. You must personally authorize acceptance before 4:00. If you do not, the offer expires and we go to trial.
```
Could say "I recommend acceptance" more direct:
"Based on these fixed numbers, I recommend you accept the offer. The expected numbers are worse at trial, and the worst trial outcome is catastrophic for your liberty and livelihood. But it is your call."
Need perhaps "if your statement 'cannot do nine years' is firm, you should accept because trial has a 55% chance of 84-108 months." Good.

Let's think if "cannot do nine years" maybe "cannot do 9 years" but plea max total 42, trial lower branch 12-18. If "will not plead if trial is basically a coin flip" - if trial 55% robbery, 45% no robbery, he might consider "basically a coin flip" and not plead. But because the no-robbery side includes 20% lesser theft with 4-10 months, not a clean win. The clean acquittal is 25%. So trial not attractive. We'll say:
"You said you won't plead if trial is basically a coin flip. It is close to a coin flip on robbery vs no robbery (55/45), but it is not a coin flip between 0 and 9 years: only 25% gives 0 additional; 20% gives 4-10 additional; 55% gives 76-100 additional. If your bottom line is 'cannot do nine years,' trial cannot promise you won't." This addresses his statement exactly.

Need maybe "no probability within range" for robbery branch: "The robbery+firearm sentence could be 84, 96, 108, or anything in between; I cannot predict. If your hard limit is nine years, the upper end is nine, so you cannot rule it out." Good.

Let's maybe include "The court must credit eight months, so if it sentences 108, you would be released after 100 more months, but total custody is 108." Good.

Need maybe "license principal livelihood" in recommendation:
"Also, a robbery conviction/plea costs you your security-officer license for 3 years after release. If the robbery branch at trial occurs, that suspension starts much later; if you take plea, it starts after 22-34 months. If you get lesser theft at trial, the suspension is only 6 months after release. That could matter to you." This captures collateral. We need perhaps not calculate.

Let's perhaps include "the firearm count is dismissed under plea" and "there are no immigration/fine/fee consequences" in recommendation? Maybe "No other collateral consequences are specified." Good.

Potential issue: "The court may reject a sentencing recommendation but must sentence within applicable range." In plea, if prosecutor recommends 30, judge can sentence 30-42. In expected comparison, should we perhaps compare "plea actual 22-34" to "trial expected 42.6-57" but if risk-averse, the "worst-case" plea 34 additional, trial worst-case 100 additional. If risk-seeking, trial's upside. Good.

Let's maybe consider "expected trial custody range after credit" if using low/high endpoints and not assuming distribution within ranges: Our formula assumes sentences at endpoints. Rule says "apply probability to low and high endpoints." Yes.

Let's maybe phrase "The expected sentence imposed" using endpoints:
"low-end expected: \(0.25(0)+0.20(12)+0.55(84)=48.6\) months; high-end expected: \(0.25(0)+0.20(18)+0.55(108)=63.0\) months." Good.

Then "after credit": "low-end expected additional: \(0.20(12-8)+0.55(84-8)=42.6\); high: \(0.20(18-8)+0.55(108-8)=57.0\)." Include acquittal 0 not shown. Good.

Potential "expected total actual including 8": "50.6-65; this is 8 + 42.6-57." Good.

Let's think if "total time from arrest" in expected can be "from arrest" or "from today"? From arrest to release = (8 already served) + additional after credit. Yes. It is equivalent to expected sentence imposed plus 8*prob acquittal. For each branch, if acquittal total=8; if convicted, total=sentence. So expected total = expected sentence + 8*0.25 = 48.6+2=50.6; 63+2=65. This matches. Good.

Need perhaps "If he is acquitted, no credit is applied; he just has no sentence. The 8 months served is not a 'sentence' and cannot be credited; no incarceration beyond time already served." Good.

Let's maybe prepare final answer in a polished manner. We'll use headings and tables. Need maintain desired oververbosity 5. Maybe final around 1200-1800 words? That might be too much? Desired 5 maybe but assignment complex. We can be thorough but concise. Around 1000-1500 words okay. We need not provide huge legal disclaimer. Use direct address.

Let's draft final:

```
Malik,

I’m writing this before the 4:00 deadline. I’m using the fixed 25/20/55 odds and the stated ranges. I am not predicting where within any range the judge will sentence.

1. The plea...
```

Let's think if "malik" as client maybe final should be "Dear Malik,"? We can write "Malik,".

Need maybe "No invented odds" maybe "Do not let anyone tell you the judge is 'likely' to give 30; we don't have that number. The plea range is 30-42." Good.

Let's maybe include all items in one coherent answer.

Potential issue: "under the offer, Malik pleads guilty to robbery. The firearm count is dismissed. The applicable custody range is 30 to 42 months, and the court must credit Malik's eight months of presentence custody." If the court must credit, but if sentenced to 30 months and served 8, "remaining" 22, but is that "from today" or "from sentencing"? Since he has served 8 months before today; if he is sentenced today, yes. We'll say "from today/sentencing, using the supplied 8-month credit."

Need perhaps "trial expected custody range before credit" not "expected trial sentence" but "expected trial custody range using only supplied endpoints and probabilities" includes "acquittal produces no sentence" and "convicted only lesser" etc. Good.

Let's perhaps include "lesser theft" "no robbery conviction" but "theft conviction" maybe a crime; license suspension six months. Good.

Need maybe "the probability of no robbery conviction and probability of no incarceration beyond time already served" if "accept plea" has 0% no robbery but "firearm count dismissed" maybe no conviction on firearm; but robbery conviction remains. Good.

Let's maybe include "If trial and lesser theft, no robbery conviction" exactly.

Potential "no incarceration beyond time already served" might be "under a sentence of 12-18 with credit, if sentence is 8? But range is 12-18, so no." We'll say "Only acquittal; lesser theft still requires 4-10 more months because the floor is 12 months." Good.

Let's think about "expected trial custody range after properly accounting for presentence credit" maybe if "lesser theft" 12-18 and credit 8, additional 4-10. Does "credit" reduce the bottom below the "applicable range"? The sentence is 12-18, then credit. Yes. Good.

Maybe include "The court may sentence within range but credit is not a downward departure; it is time served." Good not necessary.

Let's now draft final response:

---

Malik,

This is the 4:00 decision. I use the fixed probabilities and ranges. I cannot tell you a single point where the judge will sentence; the only honest numbers are ranges.

**If you accept the offer**
...
**If you go to trial**
table...
**Expected numbers**
...
**Key probabilities**
...
**Risk difference**
...
**Recommendation**
...

Let's include "firearm count dismissed" under plea.

Need maybe "Trial is basically a coin flip?" incorporate into risk difference:
"On robbery vs no robbery it is 55/45, close to a coin flip. But the no-robbery side is not clean: 20% still theft + 4-10; only 25% clean. The bad side is not a 9-year guarantee, but includes a 55% chance of 84-108. If you say you cannot do nine years, the only way to eliminate that risk is the plea."

Let's make the final not too "legalese" but appropriate.

Let's maybe use "months" rather than "years" to be precise. Include years in parentheses.

Detailed final draft:

```
Malik,

This is the decision you must personally make before 4:00. I am not accepting the offer unless you tell me to.

The plea:
- Pleads to robbery, firearm dismissed.
- Sentence range 30-42 months. Prosecutor recommends 30, but judge can go to 42; no distribution supplied.
- 8 months credit → 22-34 months remaining. Total from arrest to release: 30-42.
- License: 3 years after release. No chance of no additional custody.

Trial branches:
| outcome | prob | sentence | remaining after 8-month credit | license |
...
```

Need maybe "Total from arrest to release" for acquittal? "8 months served; released."
Let's table with "Total sentence" maybe:
- Acquittal: no sentence, 8 months served.
- Lesser: 12-18 total.
- Robbery: 84-108 total.
Maybe "remaining after credit" is enough. We don't need total from arrest in table.

Then expected:
```
Expected trial sentence (counting acquittal as 0):
0.25(0)+0.20(12-18)+0.55(84-108)=48.6-63 months.
Expected additional time after credit:
0.25(0)+0.20(4-10)+0.55(76-100)=42.6-57 months.
Expected total actual time in custody (8 + above):
50.6-65 months.
```
Need "above" in expected total "8 + additional" not "8 + expected sentence." But if read "8 + above" ambiguous. We'll say "including the 8 months already served: 50.6-65 months." Good.

Then "Key probabilities":
```
No robbery conviction at trial: 25+20=45.
No incarceration beyond time served: 25 (acquittal only).
Under plea: 0 for both.
```

Then "Risk difference":
```
Plea: certain 22-34 more months and 3-year suspension. No chance 0/4-10/76-100.
Trial: 45% chance no robbery; 25% chance no more prison; 55% chance 76-100 more and 3-year suspension after later release. Expected value favors plea, but this is not guarantee. If you need upside, trial is only way; if you cannot stand 55% bad tail, plea.
```

Need maybe "bad tail" "55% bad tail" if robbery conviction branch (55%) leads to 76-100 additional and 3-year license suspension. Good.

Then "Recommendation":
```
I recommend accepting the plea if your hard limit is avoiding the risk of 84-108 months. It guarantees a max total sentence of 42 months and no firearm conviction, at the cost of certainty of robbery conviction and 3-year suspension. But it is your call. Tell me before 4 p.m. to accept; otherwise we prepare for trial and the offer expires.
```

Need maybe "max total sentence of 42 months" - under plea yes. If judge imposes 42. Good.

Let's ensure "expected range at trial after credit" not "possible sentence" in final:
"These are weighted averages over the fixed probability branches; no single actual sentence is 42.6-57 months." Good.

Let's maybe include "No adjusting for evidence" in opening:
"I am not changing the 25/20/55 numbers based on the driver, video, or DNA; those are already in the numbers." Good. Maybe:
"I have not added or subtracted any probability." Good.

Let's think if there is a legal "duty to communicate every formal plea offer" maybe we should "I communicated the offer" in final:
"Formal offer: by 4:00 today..." yes.

Potential issue: "The Plea Offer Before Dawn" title maybe "The Plea Offer Before Dawn" question 21. No need.

Let's maybe consider if "security-officer license is principal livelihood" should affect recommendation: If trial lesser has 20% chance with only 6-month suspension vs plea 3-year; if license is very important, trial's 20% branch might be attractive, but 55% robbery branch is much worse. The expected value in months and license favors? Let's quantify "expected license consequence" perhaps? We can calculate? Not asked, but maybe "collateral consequence" need explain. Could compute expected suspension periods after release? But no distribution within custody; and suspension depends on outcome. Maybe not. Let's consider if expected license outcome:
- Plea: certain 36-month suspension after release.
- Trial expected suspension after release? If acquittal 0; lesser 6 months; robbery 36 months (but after later release). Expected months = .2*6 + .55*36 =1.2+19.8=21.0 months, lower than plea's 36. Hmm if "suspension length after release" expected, trial has lower expected suspension because 25% no suspension and 20% shorter; but if robbery conviction, suspension begins later due to prison. Is this a reason trial may be better on license? But the assignment says "expected-value analysis informs but not compel." We should be careful not to compare "expected suspension" unless asked. The license consequence in each branch is important. But if I recommend plea based on expected custody, I shouldn't ignore that trial has lower expected suspension after release. Let's think. Expected license suspension after release unconditional might be 21 months vs plea 36 months. But actual branch if convicted robbery is 36 after release; if acquitted/lesser, much less. Does this weaken recommendation? Not necessarily because custody dominates; but we should mention license risk. Malik's principal livelihood: trial offers 45% chance no robbery conviction and either no or 6-month suspension. The "expected" license suspension isn't directly comparable because a robbery conviction at trial still 3-year suspension but after release; expected months lower due to chance of no/lower suspension. We can mention "the plea has a certain 36-month suspension; trial has a 55% chance of the same 36-month suspension after a much later release, a 20% chance of only 6 months, and a 25% chance of none. In terms of raw suspension length, trial's expected suspension is lower, but that ignores the huge custody risk. It is your call." Hmm should we include expected license? Not asked. Avoid computing because problem only asks license consequence in each branch, not expected. But "risk difference" should mention license tradeoff:
- Plea: certain 3-year suspension after release.
- Trial: 55% chance of 3-year suspension after release (and release much later), 20% chance six-month suspension, 25% chance no suspension. Thus trial has chance of shorter/no suspension, but at the risk of much longer prison if robbery. This is a tradeoff. Good.

Need maybe "firearm count dismissal" is a benefit: The plea avoids a firearm conviction. The state's "firearm count" at trial is included in 84-108 aggregate. If he is convicted of robbery+firearm, "firearm count" not dismissed. Good.

Let's think if "lesser theft offense" also maybe "robbery plea or robbery conviction suspends license 3 years; lesser theft 6 months. An acquittal produces no suspension." If plea to robbery, robbery conviction suspends for three years after release. If trial robbery+firearm, same. If trial lesser theft, six months. Good.

Need maybe "The final choice belongs to Malik" in legal terms:
"Under Rule 1, I can advise but cannot consent. You are competent and understand charges; you have not authorized acceptance. I need your explicit decision before deadline." Good.

Let's maybe include "No guarantee" phrase:
"Nothing here is a guarantee. A guilty plea cannot guarantee the judge imposes 30; trial cannot guarantee acquittal; trial cannot guarantee the judge imposes 84 if convicted. These are risks and ranges." Good.

Let's maybe prepare final answer in markdown. We'll use final.

But before final, let's think if any hidden nuance about "expected trial custody range before credit" and "expected trial custody range after credit" maybe "expected" should be computed conditional on "convicted at trial" because if acquitted, no custody; but expected over all outcomes is standard. But what if "custody range" usually "if convicted" not expected? The assignment says "probability of each trial outcome" and "expected trial custody range using supplied endpoints and probabilities" likely unconditional. Good.

Let's maybe calculate conditional values in case. Should I include them in final as optional? It might confuse. But maybe Malik asked "trial is basically a coin flip"; conditional expected may be useful:
- If convicted (75%), expected sentence =64.8-84 months; after credit =56.8-76 months. But because no distribution within ranges and probabilities conditional? Let's verify:
Conditional expected sentence (among conviction only):
Low = (20/75*12 +55/75*84) = (0.2667*12 +0.7333*84) =3.2+61.6? Wait compute: 0.2667*12=3.2; 0.7333*84=61.6; sum 64.8. High 0.2667*18=4.8; 0.7333*108=79.2; sum 84.0.
Conditional expected additional after credit:
Lesser 4 (low), 10 high; robbery 76 low, 100 high. Conditional low = .2667*4 + .7333*76 =1.0667+55.733=56.8; high = .2667*10 + .7333*100 =2.667+73.333=76.0. But this assumes conditional distribution same. The unconditional expected remaining (42.6-57) is lower because includes 25% zero. If Malik asks "if I don't beat it?" But not asked. Should we include conditional "if convicted" maybe useful? It may be overkill. The assignment says "probability of each trial outcome" enough. Avoid adding not requested because could complicate. But maybe "expected trial custody range" as expected over all outcomes is likely requested; do that.

Need maybe "risk difference" maybe "plea actual 22-34; trial expected 42.6-57; but if trial and robbery, 76-100; if acquitted 0." That's enough.

Let's think if "expected total time in custody" with "acquittal" included as 8 months might be weird because if acquitted after trial, he will have served maybe >8. But using supplied 8, total expected =50.6-65. If he actually is acquitted, total actual =8 not within this expected range; expected is not actual. We'll phrase "weighted-average" and not "possible sentence." Good.

Potential issue: "The applicable aggregate custody range is 84 to 108 months" if convicted at trial of both charged counts. Does "aggregate" mean sentence may be 84 to 108, not after credit. Good.

Need maybe "no probability supplied for sentence at any particular point within a range" means even if prosecutor recommends 30, perhaps the expected sentence under plea is "30-42" but not "low/high endpoints." We shouldn't apply probabilities to endpoints in plea because no probability distribution; "expected" cannot be narrowed. We'll say "I cannot give an expected point for the plea. The judge must choose within 30-42." Good.

Need perhaps "Malik says 'I will not plead if trial is basically a coin flip, but I cannot do nine years.'" We can directly quote? Not necessary. But final can mention "You said..." Maybe:
"Your 'nine years' concern: on the trial robbery branch the sentence is 84-108 months. There is no guarantee it will be at 84; it could be 108. So if you cannot do nine years, this is the risk you would be taking." Good.

Let's perhaps include "the trial robbery branch is 55%, not 50; but close. The 45% no-robbery includes a 20% conviction for theft, not acquittal." Good.

Let's think if "expected trial custody range before credit" maybe if "probability of each trial outcome" includes "55% probability of conviction on robbery and firearm count" and "the applicable aggregate custody range" includes perhaps "armed robbery and possession during robbery"; if convicted at trial of both, no range for robbery alone. Good.

Let's maybe produce final answer now. Use markdown tables. Ensure final not too long but covers all. 

Let's write final in "Counsel Malik" voice:

```
Malik,

I am using fixed numbers ...
```

Let's formulate.

Potential final wording:

"Plea additional time after credit: 22-34 months" but if "remaining after credit" maybe "from today, assuming he is sentenced today" - I'd say "after the 8-month credit, there would be 22-34 months left to serve." Good.

Let's maybe include "credit" in "expected trial after credit" carefully:
"Acquittal has no 'credit'; it is zero additional because there is no sentence, not because credit is applied." Good.

Need maybe "The eight months will never be returned if acquitted" maybe:
"An acquittal does not 'credit'; it simply means no further custody. You cannot get the 8 months back." Good. This addresses "no credit if acquittal."

Let's include in final "I cannot tell you that if you go to trial you won't do nine years. The robbery/firearm range goes to 108 months. The plea caps at 42." Good.

Let's now produce final answer.