We need answer user's question. Need produce final with advice. Need compute carefully.

We need parse facts and rules.

Malik charged armed pharmacy robbery and possession firearm during robbery. Plea offer by 4pm: plead guilty to robbery, firearm dismissed. Applicable custody range 30 to 42 months, judge can sentence within range, recommend 30. Credit 8 months presentence custody. So plea custody before credit: 30-42 months. After credit: if sentence exactly 30 months, 22 months remaining; if 42, 34 months remaining. Since no distribution within range, state range 22-34 months remaining. If judge rejects recommendation? Under rule court may reject sentencing recommendation but must sentence within 30-42. So range remains.

Trial: if convicted both counts aggregate 84-108 months. If convicted only lesser theft, 12-18 months. Acquittal no sentence. Probabilities: acquittal 25%, lesser theft only 20%, both 55%. Eight months credited against any custodial sentence after trial. Acquittal no credit. Need expected trial custody range using supplied endpoints and probabilities. Rule 9: when no distribution, expected custody must be stated as a range by applying probability to low and high endpoints. Do not use midpoint. We have three outcomes with different sentence ranges. Need expected trial custody range after credit? Need carefully compute expected custody range before and after credit. For each outcome, after credit:
- Acquittal: 0 remaining (no sentence).
- Lesser theft only: sentence 12-18 months; credit 8, remaining 4 to 10 months (assuming credit applied against custodial sentence; if sentence 12, remaining 4, if 18, remaining 10).
- Robbery + firearm: sentence 84-108; credit 8, remaining 76 to 100 months.

Expected trial custody range: apply probabilities to low endpoints and high endpoints? Rule 9: When a sentencing range has no supplied distribution, expected custody must be stated as a range by applying the probability to the low and high endpoints. For mixture of ranges, likely calculate lower expected = sum(prob_i * lower endpoint_i), upper expected = sum(prob_i * upper endpoint_i). That yields expected before credit: lower = 0.25*0 + 0.20*12 + 0.55*84 = 0 + 2.4 + 46.2 = 48.6 months. Upper = 0.25*0 + 0.20*18 + 0.55*108 = 0 + 3.6 + 59.4 = 63.0 months. After credit: apply credit to each outcome with custody: lower expected = 0.25*0 + 0.20*(12-8) + 0.55*(84-8) = 0.20*4 + 0.55*76 = 0.8 + 41.8 = 42.6 months. Upper = 0.25*0 + 0.20*(18-8) + 0.55*(108-8) = 0.20*10 + 0.55*100 = 2 + 55 = 57 months. Alternatively if credit from expected before: expected before 48.6-63.0 minus 8? But only outcomes with custody; total probability of custody 80%; if subtract 8 for every outcome, would subtract 2 months incorrectly for acquittal. Must subtract 8*0.8 = 6.4 from expected? 48.6-6.4=42.2? Wait: 48.6 - 8*0.80 = 42.2. But my endpoint calculation gave 42.6. Let's check: lower endpoints after credit: lesser lower 4, robbery lower 76: 0.2*4=0.8, 0.55*76=41.8, total 42.6. Before lower: 0.2*12=2.4, 0.55*84=46.2 total 48.6. Difference 6.0? But probability of custody outcomes=0.8, credit=8 => 6.4. Why discrepancy? Because for lower endpoint of robbery, 84-8=76. 0.55*76 = 41.8; 0.55*84=46.2 difference 4.4. lesser difference 0.2*4=0.8; total 5.2? Wait 4.4+0.8=5.2. 0.8*8=6.4. Mist? 0.55*8=4.4, 0.2*8=1.6, total 6.0. Ah probabilities: 0.55+0.2=0.75? Wait 55% + 20% = 75%, acquittal 25%. Yes custody probability 75%, not 80. I misread. So expected before lower 48.6, after lower 42.6 difference 6.0. Upper: 63-57=6. Good. Probability of custody 75%. So expected trial custody after credit 42.6 to 57 months.

Need expected trial custody range using only endpoints and probabilities. We can show both before and after. They specifically ask:
* 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 converting analysis into guarantee.
* concrete recommendation before 4pm and decision Malik must personally make.

Need likely compute probability of no robbery conviction: trial acquittal + lesser theft only = 25+20=45%. If plea, no robbery conviction? Plea to robbery means guilty, so 0%? Question asks probability of no robbery conviction and probability of no incarceration beyond time already served. Need decide if asking across plea/trial? Could be for trial? It says license consequence in each branch; then probability of no robbery conviction and probability of no incarceration beyond time already served. Could be overall depending on choices. Need present for plea and trial.

Plea: no robbery conviction impossible: 0% (guilty plea to robbery). No incarceration beyond time already served? Plea range after credit 22-34 months; so 0% no additional incarceration (assuming judge within range, minimum 30 -> 22 beyond). If judge could reject recommendation but within range, no chance below 30. So 0%.

Trial: no robbery conviction = 45% (acquittal or lesser theft). No incarceration beyond time already served: Acquittal 25% plus lesser theft sentence after credit: 12-18, after credit 4-10, so all lesser theft outcomes still have additional incarceration (minimum 4), unless credit could cover full sentence? The lesser theft range starts at 12, credit 8, so no. So only acquittal gives no incarceration beyond time served: 25%. But wait if sentence could be 12 and credit 8 => 4, yes. Thus probability of no incarceration beyond time already served on trial = 25%. But if there is possibility of probation? Not supplied. No. So 25%. If plea, 0. If decision not made, depends. Could state if he pleads, these probabilities are 0; if trial, 45 and 25.

License consequence: Plea to robbery suspends security-officer license for 3 years after release. If trial:
- Acquittal: no suspension.
- Lesser theft conviction: 6 months suspension.
- Robbery + firearm: robbery conviction suspends 3 years after release. Does firearm count affect? Rule says robbery plea or robbery conviction suspends 3 years. Lesser theft 6 months. So if both counts, robbery conviction => 3 years after release. Need mention if acquittal no suspension. Also if lesser theft only, 6 months.

Risk difference: Need compare plea expected vs trial. Plea remaining 22-34 months, certain (within range no distribution). Trial expected after credit 42.6-57 months. Plea lower expected by 10.6 to 24.6? Compute difference: trial expected lower 42.6 vs plea range lower 22? But plea no distribution; cannot use endpoints to compare directly? We can state: Under plea, guaranteed additional custody 22-34; trial has expected 42.6-57 (range), plus chance of 76-100 months, 4-10 months, or zero. Plea avoids 3-year license? Wait plea gives 3-year license suspension, but trial has chance: 25% none, 20% 6 months, 55% 3 years. So plea guarantees 3 years suspension, trial has 75% chance of some suspension: 20% 6 months, 55% 3 years; 25% none. In terms license, trial has 45% chance of no/shorter? Actually no robbery conviction 45% includes 25% none and 20% 6 months. So trial has 45% chance of avoiding 3-year suspension, 55% chance of 3-year, 20% of 6-month. Plea: 100% 3-year. Also release: plea min 22, max 34. Trial: if both, min 76, max 100; if lesser, 4-10; if acquit 0. Expected after credit 42.6-57. The expected trial lower bound 42.6 is above plea high 34? Yes 42.6 > 34; expected upper 57 > 34. So expected trial remaining custody is higher than the entire plea range? Lower expected 42.6 > plea max 34. So risk: even at most favorable endpoint calculation, expected trial custody > plea high. But because expectation is not a guaranteed sentence, cannot say he will get 42.6; it's summary of weighted endpoints. There is 45% chance of at most 10 months additional, 25% zero, but 55% 76-100 months. The expected range after credit is 42.6-57; plea is certain 22-34. The difference: trial's weighted expected lower endpoint exceeds plea's maximum remaining by 8.6 months; upper endpoint exceeds by 23 months. Wait 42.6 -34 = 8.6. 57 -34=23. If comparing to plea midpoint? Not use. Could also compare expected before: plea before 30-42; trial before expected 48.6-63.0. After credit plea 22-34; trial after 42.6-57.

Malik says cannot do nine years, won't plead if basically coin flip. Need tell real numbers. Nine years = 108 months max trial, expected range 42.6-57 months (3.55-4.75 years) after credit. But 55% chance 76-100 months (6.3-8.3 years). That's less than nine but can be near. He may be saying cannot do nine years; the maximum is 9 years, expected not nine. But 55% chance of long. The plea is max 34 months remaining (2.83 years), plus 3-year license suspension after release. Trial has expected 42.6-57 months remaining (3.55-4.75 years), with 55% chance 76-100 (6.3-8.3 years) and 3-year license; 45% chance lower/no robbery (25% no jail, 20% 4-10 months + 6-month license). Since his livelihood is license, need consider. If plea: license suspended 3 years after release; release after 22-34 months. So license back after 50-62 months from now? Wait if suspension starts after release and presentence time? Need be careful. License consequence: suspended for 3 years after release. If plea sentence 30-42 months, after credit 22-34. If released after that, then 36 months suspension, total no license from now? If he's in custody, does license suspended during custody? It says suspends for three years after release. Could imply starts after release, but during custody he cannot work? We can state as rule: 3-year post-release suspension; if after 22-34 months, 36 months additional suspension, so if counting from today, up to 70 months? Actually 22+36=58, 34+36=70 months from today (if suspension starts at release). But perhaps suspension from plea or release? It says after release. We should not overcomplicate. For lesser theft: 6 months after release (if 4-10 remaining, then 6 months). Acquittal none.

Need concrete recommendation before 4pm. Based on expected value and his constraints: "I will not plead if trial is basically a coin flip, but I cannot do nine years. Tell me real numbers, not what you think sounds safe." Need advise likely accept plea? Need weigh. The plea is lower expected custody and avoids chance of 6.3-8.3 years, but guarantees 3-year license suspension and 22-34 months remaining. Trial has 45% chance no robbery conviction (25% free, 20% short) and 55% long. Expected trial custody higher. His livelihood license: plea 100% 3-year suspension; trial 55% 3-year, 20% 6-month, 25% none. If his license is principal livelihood, the 45% chance of avoiding 3-year suspension and 25% no incarceration might be valuable. But if he cannot do nine years, the 55% chance of 76-100 months may be too risky. The question asks concrete recommendation before 4pm and decision Malik must personally make. We need make a recommendation, not just neutral? Assignment says counsel must advise, final choice defendant. We can recommend: accept plea if his top priority is avoiding 6-8+ years and he is risk-averse to long sentence; but if his principal livelihood license and he values 45% chance of no 3-year suspension/no robbery conviction, trial may be consistent. Need concrete recommendation? We should choose one based on numbers. Need be careful with rule 10: expected-value informs but does not compel risk-neutral defendant; explain probabilities. "Concrete recommendation before 4pm" likely must be: accept the plea? Let's reason.

Malik's statements: "I will not plead if trial is basically a coin flip, but I cannot do nine years." Trial not coin flip for acquittal: 25% acquittal, 45% no robbery. But high-risk 55% both counts. "cannot do nine years" perhaps maximum 108 months = 9 years, expected around 3.5-4.75 years. But 55% chance 76-100. He may be okay with expected less than nine? He asks real numbers. He is competent, not authorized counsel. We need recommend before deadline. We need not assume his risk preferences beyond statements. He says cannot do nine years; if he means cannot accept 9-year exposure, plea avoids. He also says won't plead if trial is basically a coin flip; trial no robbery 45%, so not coin flip? But the bad outcome 55% is worse than coin flip. We should say trial is not a coin flip: 55% chance of the worst outcome, 45% chance no robbery conviction, 25% chance zero jail. If his "cannot do nine years" is a hard limit on exposure, plea is the only way to cap at 34 months remaining. If he can tolerate 55% chance of 76-100 months for chance of zero/short and avoiding license, trial is his. But "concrete recommendation" likely: Based on expected custody and his stated inability to handle a nine-year outcome, I would advise him to accept the robbery plea by 4:00, because it converts a 55% chance of 76-100 months into a certain 22-34 months, and the license downside (3-year post-release suspension) is the price. But must emphasize final choice his, and if he values 45% chance to avoid 3-year license more than avoiding 6-8 years, he may reject. However "concrete recommendation" may require one: accept plea. Let's see.

Could there be nuance: plea custody before credit 30-42; after credit 22-34. Trial expected after credit 42.6-57. Plea expected? Since no distribution, cannot give expected plea as number; range certain. Trial expected is above plea high. This strongly suggests plea if risk-averse and "cannot do nine years". But license: plea guarantees 3-year suspension. If principal livelihood, maybe risk trial for 45% avoid 3-year. Expected license consequence? No expected value needed? Could compute expected suspension months? Not asked, but might inform. Let's consider license expected: Plea: 36 months (100%). Trial: 0.25*0 +0.20*6 +0.55*36 = 1.2 +19.8 =21.6 months expected. So trial has lower expected license suspension. If livelihood important, trial may be better expected license, but much higher expected jail. Need mention. But no expected value for license? Could state not converting to guarantee. The question specifically asks license consequence in each branch, not expected license. Could mention as part risk.

Need ensure no midpoint. For plea range after credit, if we say "certain 22-34". Do not say 28 expected. For trial expected range, use endpoints. Need show formula.

Potential issue: "expected trial custody range using only supplied endpoints and probabilities" Could they expect: For each outcome: 25% x 0, 20% x 12-18, 55% x 84-108. The expected range: lower = 0.25*0 + 0.20*12 + 0.55*84 = 48.6; upper = 0.25*0 + 0.20*18 + 0.55*108 = 63.0. After credit: need properly account. We did. But maybe they want expected trial custody range before credit: 48.6-63.0; after credit: 42.6-57.0. Need label months.

Potential issue: presentence credit against any custodial sentence after trial. If sentence less than 8? Not possible; lesser min 12. If acquittal, no credit. Good.

Potential issue: "The court may reject a sentencing recommendation but must sentence within the applicable range stated below." For plea, prosecutor recommends 30, but judge may 30-42. We should not say 30 likely; state could be any in range. Since no distribution, cannot estimate chance of 30. So plea remaining 22-34.

Potential issue: "armed pharmacy robbery and possession of a firearm during the robbery" Plea: firearm dismissed. If trial convicted both counts aggregate range 84-108. If convicted only lesser theft, 12-18. There is no outcome: convicted robbery only without firearm? Not supplied. The fixed probabilities sum to 100: acquittal, lesser theft only, both. So no need.

Potential issue: "probability of no robbery conviction" Under trial: 45%. Under plea: 0. Could also ask "probability of no robbery conviction" maybe if he goes to trial? We'll include both.

Potential issue: "probability of no incarceration beyond time already served" Under trial: 25% (acquittal only). Under plea: 0. However if sentence on lesser theft could be 8 or less? No, range 12-18, so no. If judge gives 12 and credit 8, 4. So 0 for lesser. Good.

Potential issue: license if trial both counts: Does firearm conviction add separate license suspension? Rule only says robbery plea/conviction 3 years; lesser theft 6 months. If both counts includes robbery, so 3 years; no separate specified. We should say no additional license consequence is supplied. Good.

Potential issue: "after release" for license. If in pretrial custody, release maybe after sentence. We can say "a 3-year suspension attached to a robbery conviction would run after any release; it does not itself add months to the jail term." It might start at release, but if he is already in custody before plea? Presentence custody might not count as release. We don't need compute total from today unless asked. But could include illustrative: If plea results in 30 months, 22 remaining, then 36-month post-release license suspension; if 42, 34 remaining then 36. But be careful: if suspension is "after release," total license loss from today could be 22+36 to 34+36 = 58-70 months, but during custody he's not working anyway? Maybe not necessary. It could be useful.

Potential issue: recommendation. Need maybe use "I would advise Malik to accept the plea if he treats 76-100 months as intolerable, because the numbers show the plea caps additional time at 34 months and trial has a 55% chance of 76-100 months. But because his license is principal livelihood, and trial gives 45% chance of no 3-year suspension and 25% chance no jail, if he values the chance of clearing his name more than avoiding long custody, he can rationally reject. The concrete recommendation: given his 'cannot do nine years' and not coin flip? Hmm.

Let's read user: "Counsel Malik on: ... The concrete recommendation before 4:00 p.m. and the decision Malik must personally make." They likely expect a client advice memo. We should produce structured answer with headings. Need be precise, no invented odds. Need state not guarantee. Need maybe include a table.

Let's think if there is a subtle expected custody calculation after credit: Rule 9 says "When a sentencing range has no supplied distribution, expected custody must be stated as a range by applying the probability to the low and high endpoints. Do not use the midpoint as though it were a predicted sentence." This might mean for each range, expected low and high as we did. But for trial mixture, maybe need expected low = P(acq)*0 + P(lesser)*12 + P(both)*84 = 48.6; expected high = P(acq)*0 + P(lesser)*18 + P(both)*108 = 63.0. After credit: Need "properly accounting" maybe should subtract 8 months from each outcome with sentence before weighting. We did. But alternative: Apply probabilities to endpoints after credit: same. Good.

Could there be an expected range for plea? The plea has no probability distribution over outcomes; it's a certain plea but sentencing range uncertain. Rule 9 applies to sentencing range with no supplied distribution. Should we state plea expected custody range? It is just 30-42 before credit, 22-34 after. They asked plea custody range before and after. Not expected. Do not compute midpoint. Good.

Need include risk difference: Maybe use table comparing guaranteed plea vs trial outcomes:
Plea:
- Robbery conviction: 100%
- Additional custody: 22-34 months (certain within range)
- License: 3 years after release (100%)
- No robbery conviction: 0%
- No additional incarceration: 0%

Trial:
- Acquittal: 25% -> 0 additional, no license, no robbery conviction
- Lesser theft: 20% -> 4-10 months additional, 6-month license, no robbery conviction
- Robbery+firearm: 55% -> 76-100 months additional, 3-year license, robbery conviction
- No robbery conviction: 45%
- No additional incarceration: 25%
- Expected additional custody: 42.6-57 months
- Expected before credit: 48.6-63.0 months

Risk difference:
- Plea converts uncertain trial to known range 22-34; avoids 55% chance of 76-100. But gives up 45% chance of no robbery (25% zero, 20% 4-10) and guarantees 3-year license suspension. Trial expected additional custody is above the plea's upper end: 42.6-57 vs 22-34. In the weighted endpoint comparison, the trial's low expected endpoint is 8.6 months more than the plea's maximum; the high expected endpoint is 23 months more. But expected range is not a predicted sentence; it aggregates endpoints.
- For license: plea 100% 3-year; trial 55% 3-year, 20% 6-month, 25% none. So trial has 45% chance of avoiding 3-year; but if 55% outcome, same license as plea plus much more jail.
- No incarceration beyond time served: plea 0, trial 25.

Concrete recommendation: Need formulate. Let's decide. Could say: "On the numbers, the plea is the lower-custody option and is the only way to cap the additional time at 34 months. If Malik says he cannot do nine years and is treating the 55% chance of 76-100 months as unacceptable, I would advise him to accept the plea by 4:00. If, after understanding the 55% long-outcome risk, he nonetheless values the 45% chance of no robbery conviction / 25% chance of no jail and the chance to avoid a 3-year license suspension more, then rejecting is a rational choice. But if he asks for a concrete recommendation from counsel based on his stated inability to handle a nine-year outcome, my recommendation is to plead to robbery and let the firearm count be dismissed, understanding the judge can impose 30-42 months (22-34 after credit) and the 3-year post-release license suspension."

Would that satisfy? Yes. Need maybe say "Do not plead if his priority is preserving license; trial is the only chance to avoid 3-year suspension, with 45% chance (25 no suspension, 20 six months)." But concrete recommendation maybe conditional? They asked concrete recommendation. Could state one while acknowledging final choice. We can say "My concrete recommendation is to accept the plea, subject to his personal risk tolerance; if he prioritizes license over jail, he may choose trial." But "concrete" should not be too equivocal. We can state: "I recommend he accept the plea." Then decision he makes: accept or reject; if reject, offer expires at 4 and goes to trial. Need maybe mention he has not authorized counsel; counsel cannot accept without him. Need maybe say "He must personally say 'I accept' or 'I reject' before 4; if reject, offer is gone and trial proceeds with those odds." Also final choice belongs to defendant.

Need perhaps include "material consequences" all. Good.

Let's consider if any ethical issue: Need not use midpoint. Need not add facts. Need communicate every formal plea offer. We are advising. Need maybe state "I am not predicting the judge; no supplied probability for any point in 30-42." Good.

Let's verify calculations:
Trial before credit:
Acquittal: 0.
Lesser: 12-18 *20% = 2.4 to 3.6.
Both: 84-108 *55% = 46.2 to 59.4.
Sum = 48.6 to 63.0.
After credit:
Acquittal: 0.
Lesser: (12-8)=4 to (18-8)=10 *20% = 0.8 to 2.0.
Both: (84-8)=76 to (108-8)=100 *55% = 41.8 to 55.0.
Sum = 42.6 to 57.0.
Plea after credit: 30-8=22 to 42-8=34.
Plea before: 30 to 42.

Expected trial range after credit lower 42.6. Compare to plea high 34: +8.6. Compare to plea low 22: +20.6. Upper +35 vs 22, +23 vs 34.
If use before credit: trial expected 48.6-63 vs plea 30-42. Lower +18.6 vs plea low, +6.6 vs plea high. Upper +21 vs low, +21? 63-42=21, 63-30=33. After credit maybe more meaningful because time already served. Good.

License expected if wanted:
Trial expected months = .25*0 + .20*6 + .55*36 = 21.6. Plea =36. If suspension after release, not direct. Could mention "If one were to weight only license lengths (not recommended as a standalone), trial's expected suspension is lower, but the custody risk is much higher." But assignment doesn't ask expected license; adding may be okay if not overcomplicate. Need avoid risk-neutral? Rule 10 says expected value informs but does not compel risk-neutral defendant. We can mention not to over-rely.

Potential nuance: "The court may reject a sentencing recommendation but must sentence within the applicable range stated below." If judge rejects recommendation, could impose 42. We must not assume 30. We can say "The prosecutor's 30-month recommendation is not a guarantee." Good.

Potential nuance: "The applicable custody range is 30 to 42 months, and the court must credit Malik's eight months of presentence custody." Does credit reduce the range endpoints? Yes. If sentence 30, credit 8, time to serve 22. If sentence 42, 34. But could presentence custody credit be applied such that if sentence 30, he gets 8 months credit, yes. If he remains in custody, he may be released after 22 months of sentence, i.e., 14 months from now? Wait he already spent 8 months. Total sentence 30 means 22 more months from now. So 30 total from original? Yes.

Potential nuance: "No credit is applied to an acquittal because no sentence exists." Good.

Potential nuance: "If Malik is convicted at trial of both charged counts, the applicable aggregate custody range is 84 to 108 months. If he is convicted only of the lesser theft offense, the range is 12 to 18 months." If trial convicted both, does the eight months credit apply to aggregate? Yes, against any custodial sentence after trial. So after credit 76-100.

Potential nuance: "A robbery plea or robbery conviction suspends Malik's security-officer license for three years after release. A lesser-theft conviction suspends it for six months. An acquittal produces no suspension." If trial convicted both, robbery conviction => 3 years. If trial convicted lesser only, 6 months. If plea, 3 years. Good.

Potential nuance: "There is no additional charge, mandatory fine, immigration consequence, or fee shifting." So only these consequences. We can mention no other material consequences supplied.

Potential nuance: "The supplied probabilities already account for eyewitness etc. Do not add/subtract." We should not comment on evidence affecting odds. Maybe state we rely only on fixed 25/20/55.

Potential nuance: "Malik is competent, understands charges, and has not authorized counsel to accept the offer." So final decision his; cannot accept for him. Need maybe say "I cannot and will not accept for him; he must communicate his decision to me before 4:00." Good.

Need maybe include a "bottom line" at top or end. Desired oververbosity 9, so detailed. But not too long? We can provide thorough memo. Use bullet points and tables. Need ensure all requested items covered explicitly.

Let's design final answer:

Title: Advice to Malik on plea offer (fictional Harrow)

Start: "I am advising you only on the supplied facts/odds. No probability within ranges. Final decision is yours."

1. Plea offer and custody:
- Offer: guilty plea to robbery; firearm dismissed; prosecutor recommends 30; judge may impose 30-42.
- Before credit: 30-42 months.
- 8 months credit: 22-34 months additional. The judge's choice within range uncertain; no supplied odds for 30 vs 42. If 30 => 22; if 42 => 34.
- Collateral: 3-year license suspension after release. No other supplied.

2. Trial outcomes and probabilities:
Table:
Outcome | probability | sentence before credit | after 8mo credit | license
Acquittal 25% | 0 | 0 | none
Lesser theft only 20% | 12-18 | 4-10 | 6 months
Robbery+firearm 55% | 84-108 | 76-100 | 3 years after release
Sum 100%.

3. Expected trial custody range:
Explain method: apply probabilities to low and high endpoints, not midpoint.
Before credit:
Low = .25*0 + .20*12 + .55*84 = 48.6 months.
High = .25*0 + .20*18 + .55*108 = 63.0 months.
So expected trial custody before credit: 48.6-63.0 months (weighted endpoint range), not a guaranteed 48.6 or 63.
After credit:
Low = .25*0 + .20*(12-8) + .55*(84-8) = 42.6.
High = .25*0 + .20*(18-8) + .55*(108-8) = 57.0.
So expected trial custody after credit: 42.6-57.0 months.
Note: This does not mean he will get 42.6; actual outcomes are 0, 4-10, 76-100.

4. License consequence in each branch:
Maybe table above plus summary: Plea 100% 3-year. Trial: 25 none, 20 six months, 55 three years. If both counts, 3-year due to robbery; no separate license consequence supplied.

5. Key probabilities:
- No robbery conviction: Plea 0; Trial 45 (25 acquittal +20 lesser). If he is deciding, choosing trial gives 45, plea gives 0.
- No incarceration beyond 8 months already served: Plea 0 (minimum 22 additional); Trial 25 (acquittal only). Lesser still 4-10 additional.
- Chance of at least 76 months additional: 55%.
- Chance of 4-10 additional: 20%.
- Chance of zero additional: 25%.

6. Risk difference:
Compare:
- Plea: certain 22-34 months; 100% 3-year license.
- Trial: expected after credit 42.6-57; weighted endpoint low is 8.6 months above plea's maximum 34; high is 23 above. But not guarantee.
- Trial upside: 25% zero, 45% no robbery, 45% avoid 3-year license (25 none, 20 6-month), 20% only 4-10.
- Trial downside: 55% 76-100 months and 3-year license. Plea caps at 34 and avoids that 55% long exposure, but gives up upside.
- If "nine years" is hard ceiling, plea avoids 9-year max; trial max 100 months after credit (8 years 4 months?) Wait 100 months is 8 years 4 months, not nine. Before credit max 108 (9 years), after credit 100 (8 years 4 months). Need be careful: "I cannot do nine years." The trial range after credit max 100 months (8 years 4 months) if judge imposes 108 and credit 8. Before credit max 108. If he means total sentence, max 9 years; if additional after credit, max 100 months. We can state: The worst supplied trial outcome is 108 months total, reduced by 8 to 100 months remaining. So if he cannot accept even a 100-month remaining exposure, plea caps at 34. But "cannot do nine years" maybe he can't do 108. Plea avoids. The expected trial after credit 42.6-57 is 3.55-4.75 years. But 55% chance 76-100 (6.3-8.3). Good.
- License tradeoff: Plea guarantees 3-year post-release suspension; trial has 55% same, 20% 6 months, 25% none. If livelihood, trial's license upside may matter; plea's custody downside avoided.

7. Concrete recommendation:
Need phrase. Let's write:
"Given the numbers and your statement that you cannot do nine years, my concrete recommendation is to accept the plea by 4:00 p.m. The plea is the only path that caps additional time at 34 months and eliminates the 55% chance of 76-100 months. The cost is a robbery conviction and a 3-year post-release license suspension. That recommendation is driven by your stated limit on long custody; it is not a legal compulsion. If, after understanding the 55% chance of 76-100 months, you decide the 25% chance of zero time and 45% chance of no robbery/3-year license are worth more to you, you may choose to reject the offer and go to trial. But you must personally make that choice before the deadline; I cannot accept or reject for you. If you want the plea, tell me you authorize me to accept; if not, tell me you reject and I will let the offer lapse."

Need perhaps be more nuanced: The plea also guarantees 3-year license, which if principal livelihood could be severe. But the question asks concrete recommendation; we can say "I recommend accept only if he prioritizes avoiding long custody; if he prioritizes license, trial is rational." But that's not concrete? We can make concrete: "I recommend he accept, because his stated 'cannot do nine years' and the 55% long-sentence risk make the plea the lower-risk custody choice; however if he tells me the license is more important than avoiding 76-100, then I would support his choice to go to trial." Hmm.

Maybe the correct answer from legal ethics / risk communication: Counsel should not decide for client; must provide all info. But assignment asks "concrete recommendation before 4pm and decision Malik must personally make." It might expect: "Recommend the plea based on expected values and his stated constraints; but final decision his." Good.

Let's ensure no use of "coin flip". We can say trial is not a coin flip: 55% worst, 45% no robbery; but it is a high-risk lottery with 25% zero. He said won't plead if basically coin flip; we can clarify: The probabilities are 25/20/55, not 50/50. The chance of no robbery is 45%, but the chance of the worst outcome is 55%. So if by coin flip he means even chance of acquittal, it's not; it's worse on the long-sentence side. Good.

Need maybe include "material sentencing, trial, and collateral consequences" all. Good.

Could there be an issue with "expected trial custody range after properly accounting for presentence credit" if the expected range should be derived by subtracting 8 months from the expected before range? But because acquittal no credit, not simply subtract 8 from all. We did proper. Could mention "I do not subtract 8 months from the acquittal branch." Good.

Let's double-check expected after credit by alternate method: Expected before credit = 48.6-63.0. Probability of custody = 75. Expected credit if custody = 8*0.75 = 6.0. Subtract: 42.6-57.0. Good. Nice to mention.

Need maybe include all numbers in months and maybe years for client? Could include months and approx years, but careful not to imply precision? It's okay. 42.6 months = 3.55 years; 57 = 4.75 years. 22-34 = 1.83-2.83. 76-100 = 6.33-8.33. But maybe avoid approximate or include in parentheses.

Potential edge: The plea custody range before and after credit: before credit 30-42; after 22-34. But if he has already served 8, "before credit" could be sentence length, not time to serve. We'll label "sentence" and "time remaining/additional". Good.

Potential edge: "The court may reject a sentencing recommendation but must sentence within the applicable range stated below." If judge rejects 30 recommendation, can sentence 42. Need state no probability for recommendation. Good.

Potential edge: "The final choice belongs to the defendant." We'll emphasize.

Potential edge: "Counsel must communicate every formal plea offer" We can quote offer. Good.

Potential edge: "Do not invent different odds or assume where a judge will sentence within a stated range." We won't. We might say "No supplied probability for 30 vs 42." Good.

Potential edge: "Do not add or subtract probability for facts." We won't discuss evidence. Good.

Potential edge: "Expected-value analysis informs advice but does not compel a risk-neutral defendant." We'll state that.

Let's consider if there is a possibility of "no incarceration beyond time already served" on trial if lesser theft sentence 12 and credit 8 = 4; no. If acquittal, yes. What about if he is released after trial before sentence? Not relevant.

Potential edge: "security-officer license is his principal livelihood." We need factor in advice. Could say: The plea's license consequence is severe and certain. Trial has 45% chance to avoid 3-year suspension and 25% no suspension. If he can live with 22-34 months, the plea may be better for custody; if he cannot live without license for 3 years, trial may be rational despite higher expected jail. But the assignment asks concrete recommendation. Maybe we can say: "Because he has identified both a hard line ('cannot do nine years') and a livelihood concern, the decision is genuinely a tradeoff. A concrete recommendation must be tied to which concern controls. On the numbers alone and given 'cannot do nine years,' I recommend pleading. If he tells me his license is the dominant value, I would advise him that trial is the only way to have a 45% chance to avoid the 3-year suspension, but with 55% chance of much longer jail. He must choose." But "concrete recommendation before 4pm" maybe wants a single recommendation. We can still give single while acknowledging.

Let's think if a risk-averse expected value would pick plea? Compare expected remaining custody: plea range 22-34, trial expected 42.6-57. Plea lower. But expected utility with license: Need assign value to months vs license. Not given. Since license principal livelihood, cannot ignore. But no values. We can still recommend based on his statement cannot do nine years. If he cannot do nine years, plea. If he can tolerate expected 4.75 but not max? He says cannot do nine years, maybe means max. Plea. Good.

Need maybe mention "The offer expires at 4; if he doesn't decide, treat as rejection?" Not necessarily. We can say he must communicate before 4; if no decision, offer expires. Good.

Let's maybe produce final with a "Numbers" table, then "What that means for your decision", then "Recommendation". Need include formulas.

Let's draft final in detail:

```
Bottom line: The plea means 22-34 months more time and a certain 3-year post-release license suspension. Trial gives: 25% no jail/no license, 20% 4-10 months + 6-month license, 55% 76-100 months + 3-year license. Trial's expected additional custody is 42.6-57 months, using endpoint method. Given your statement that you cannot do nine years and the 55% chance of 76-100 months, I recommend accepting the plea if your priority is capping custody; but if avoiding the 3-year license suspension is worth the 55% long-sentence risk, you may reject. The decision is yours before 4.
```

But need be careful: "expected additional custody 42.6-57" might sound like a guarantee. We'll qualify: "weighted endpoint range, not a predicted sentence."

Let's include formulas:
```
Trial before credit low = (0.25)(0)+(0.20)(12)+(0.55)(84)=48.6
high = (0.25)(0)+(0.20)(18)+(0.55)(108)=63.0
After credit low = (0.25)(0)+(0.20)(4)+(0.55)(76)=42.6
high = (0.25)(0)+(0.20)(10)+(0.55)(100)=57.0
```

Maybe include "All in months." Good.

Risk difference table:
```
Feature | Plea | Trial
Additional custody | 22-34 certain within range | 0 (25%), 4-10 (20%), 76-100 (55%); expected 42.6-57
Robbery conviction | 100% | 55%
No robbery conviction | 0% | 45%
No additional incarceration | 0% | 25%
License | 3 yrs after release (100%) | none 25%, 6 mo 20%, 3 yrs 55%
```

Need maybe include "firearm count dismissed on plea; on trial if both counts, aggregate range includes firearm." Good.

Potential issue: If plea, robbery conviction suspends license for three years after release. Does that mean if he is sentenced 30-42, he may be released after 22-34 months, then license suspended 3 years; total without license from release 36 months. But if he is in custody for pretrial, he cannot work anyway. Could state "If you are released after 22 months, the 3-year suspension would begin after release; if after 34 months, likewise. I am not told whether the suspension runs during any remaining custody or post-release; under the rule stated, it is 3 years after release." Wait rule says "after release". We should not assume it doesn't run during custody; it starts after release. If he is currently in presentence custody, he is not released until sentence ends. So from today, if 30-month sentence, he has 22 months to release, then 36 months no license = 58 months from now. If 42, 70 months. But does "suspends his license for three years after release" mean the suspension period is three years, starting at release. Yes. Could mention as consequence: "For planning, that means the license loss would extend 36 months beyond release; under the supplied rule, it is tied to release, not to the presentence credit." But if he is already in custody, his license is likely suspended during detention? The rule doesn't say. Better not invent. We can say "The stated consequence is a three-year suspension after release; I have not been given a rule making it run during custody, so I will not count it as extra jail time." Good.

Could include "no other collateral consequences are supplied (no fine, immigration, fees)." Good.

Let's think if "probability of no incarceration beyond time already served" on plea: If judge imposes 30 and credit 8, 22. But what if he is released on other grounds? Not supplied. So 0.

Could include "probability of no robbery conviction" if trial: 45; if plea: 0. If he goes to trial and convicted lesser, that's not robbery. Good.

Could include "probability of a 3-year license suspension": plea 100; trial 55. "Probability of any license suspension": plea 100; trial 75. Maybe useful. The question only asks license consequence in each branch, not probability. But can include.

Need maybe include "The driver's credibility etc. already accounted for; I am not adjusting." We can state in note.

Potential issue: "expected trial custody range using only supplied endpoints and probabilities" Could they want no credit? Yes. We will label before and after. Good.

Potential issue: "expected trial custody range after properly accounting for presentence credit" Could they want after credit to be a range derived from after-credit endpoints as we did. Good.

Potential issue: "risk difference between plea and trial without converting the analysis into a guarantee." We will explicitly say expected numbers are not predictions; plea range certain but judge within range unknown; trial actual outcomes discrete.

Potential issue: "concrete recommendation before 4:00 p.m. and the decision Malik must personally make." We'll end with action: "If you choose plea, you must authorize me in writing/phone before 4; if not, tell me reject. I will not accept without you." Good.

Let's consider if we need to mention "State of Harrow" fictional? Not necessary.

Let's maybe include a short "Why I am not using midpoint" note. Good.

Let's evaluate if final answer may be too long. Desired oververbosity 9, okay.

Potential alternate recommendation: Maybe we should not recommend plea because of license principal livelihood and expected license lower. Let's examine. If we assign utility: Jail months and license months. If each month of license lost equivalent to jail month, trial expected total cost = expected jail 42.6-57 + expected license 21.6 = 64.2-78.6; plea = 22-34 + 36 = 58-70. Plea may still lower expected total at lower bound? 58 vs 64.2; but at upper bound 70 vs 78.6. If license more valuable, trial. But no values. Malik says cannot do nine years, so plea. Good.

But "principal livelihood" might make 3-year license suspension worse than 34 months jail? If so trial might be better. But expected jail trial is much higher. A rational risk-neutral with equal month values would compare expected jail + license? But expected license calculation uses lengths; plea 36, trial 21.6. If equal value, plea expected total (using endpoints?) lower? Need not compute. But if license more valuable, trial. Since he says cannot do nine years, likely custody risk dominates.

The assignment may be testing that counsel must not coerce; must present tradeoffs. But asks concrete recommendation. In legal ethics, attorney can recommend but not decide. We can recommend based on client's stated goals. Good.

Let's maybe phrase recommendation as conditional but concrete: "My recommendation is to accept the plea unless Malik tells me, after hearing the 55% risk, that the license is more important to him than avoiding 76-100 months. Given his stated 'cannot do nine years,' I would advise him to accept now." That is concrete enough? Maybe.

Let's include "If he rejects, he cannot later take the offer after 4 without new negotiations." Good.

Need maybe mention "The prosecutor's recommendation 30 months is material but not controlling." Good.

Let's ensure final doesn't say "guaranteed 22-34" in a way that implies guarantee of exact range? It is certain he will get some sentence within 22-34 after credit; the exact point uncertain. We can say "certain to be within". Good.

Potential issue: "The court may reject a sentencing recommendation but must sentence within the applicable range stated below." If court rejects recommendation, can it sentence below 30? No, range 30-42. Good.

Potential issue: "A guilty plea must be knowing and voluntary." We can say to accept, he must enter plea knowingly/voluntarily after advising. Good.

Potential issue: "Counsel must advise material sentencing, trial, and collateral consequences." We include.

Let's maybe include "No probability is supplied for the judge's exact plea sentence; therefore I cannot say 30 months is likely." Good.

Let's draft final in polished form:

```
I will use only the supplied probabilities and endpoints. All numbers are months.

1. Plea offer
...
```

Use table.

Need maybe include "Before credit" vs "After credit" columns.

Let's write final now. Ensure no analysis in final. Use final. But before final, maybe think if any hidden trap: The plea range is 30 to 42, credit 8. Expected trial custody range using only endpoints and probabilities. Could there be a need to compute expected plea custody range? Not asked, but maybe for risk difference. We can say plea has no expected point because no distribution; range 22-34. Do not compute midpoint. Good.

Could there be a trap: "If Malik is convicted at trial of both charged counts, the applicable aggregate custody range is 84 to 108 months. If he is convicted only of the lesser theft offense, the range is 12 to 18 months." If he is convicted of robbery only (firearm not) not a trial outcome supplied. The probability of both 55, lesser 20, acquittal 25. Good.

Could there be a trap: "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." We applied. Good.

Could there be a trap: "A robbery plea or robbery conviction suspends Malik's security-officer license for three years after release. A lesser-theft conviction suspends it for six months. An acquittal produces no suspension." If trial both counts, the firearm count might also be a separate offense? Not specified. We say only robbery consequence. Good.

Could there be a trap: "When a sentencing range has no supplied distribution, expected custody must be stated as a range by applying the probability to the low and high endpoints. Do not use the midpoint as though it were a predicted sentence." For plea range, no probability but range. We don't use midpoint. For trial expected, use endpoints. Good.

Could there be a trap: "risk difference without converting analysis into a guarantee." We'll be explicit.

Could there be a trap: "concrete recommendation before 4pm and decision Malik must personally make." We'll state: accept or reject; if accept, must personally authorize; if reject, offer expires. Good.

Let's maybe include a "Plain-English summary" at top. Good.

Potential issue: "I recommend accept" might be seen as counsel making choice. We'll say "My recommendation, not the decision, is..." Good.

Let's think if there is any need to calculate "probability of no incarceration beyond time already served" if plea: If sentence 30 and credit 8 = 22. But what if presentence custody is credited such that he has already served 8 of the 30, so time remaining 22. Yes.

Potential issue: "No incarceration beyond time already served" could include if sentence is 12 months on lesser and 8 credit, but he might be released on credit before trial? No, after trial sentence; he remains in custody? It says credited against sentence. If he is in custody, 8 already served, 4 left. So still incarceration beyond time already served. Good.

Potential issue: "probability of no robbery conviction" on trial includes acquittal and lesser theft. If he is acquitted of both, 25; if convicted lesser, 20. Total 45. Good.

Potential issue: "probability of no incarceration beyond time already served" on trial could include lesser theft if sentence 12 and credit 8? No. Good.

Potential issue: "expected trial custody range after credit" maybe they want "42.6 to 57.0 months of expected remaining custody" but if he is currently in custody, "remaining" maybe not exactly if he is released for other reasons. But fine.

Potential issue: The 8 months presentence custody is credited after trial. If he is acquitted, no credit, but he still spent 8 months in custody; "no incarceration beyond time already served" yes, he has served 8. Good.

Potential issue: "license consequence in each branch" If plea: 3 years after release. If trial acquittal: none. If lesser: 6 months (probably after release? Rule says suspends it for six months, not explicitly after release; maybe just six months. We can say "six-month suspension (stated as six months; I have no supplied rule tying it to release)." But to be consistent, we can say "six months" not after release. For robbery, after release. Good.

Potential issue: If trial both counts, if robbery conviction, 3 years after release. If the firearm count also results in separate suspension? Not supplied. Good.

Let's maybe include "I am not assigning a probability to a 30-month plea sentence; the range is 30-42." Good.

Let's formulate final elegantly:

```
All figures are months unless noted.

Bottom line ...
```

Need ensure final answer covers each bullet exactly. Use headings matching assignment maybe.

Let's produce final.