Exercise 1: Finding the Crossover Point — Possible Solution ==================================================================== METHOD ------------------------------ Setting with_adr_cost == without_adr_cost and solving for reversal_cost: ADR_COST + wrong_prob * ADR_RISK_REDUCTION * R = wrong_prob * R 2 + 0.3*0.5*R = 0.3*R 2 + 0.15*R = 0.3*R 2 = 0.15*R R = 2 / 0.15 = 13.33 hours RESULTS (verified numerically) ------------------------------ reversal_cost=13: with_adr=3.95, without_adr=3.90 -> no ADR better reversal_cost=13.33: with_adr=4.00, without_adr=4.00 -> break-even reversal_cost=13.34: with_adr=4.00, without_adr=4.00 -> ADR better reversal_cost=20: with_adr=5.00, without_adr=6.00 -> ADR better The crossover point is exactly 13.33 hours of reversal cost - below it, skipping the ADR is the better expected-value choice; above it, writing the ADR is. WHY THIS WORKS AS AN ANSWER ------------------------------ This turns the chapter's own two illustrative examples (1-hour and 200-hour reversal costs) into an actual, general decision rule: any decision whose reversal would cost more than roughly 13-14 hours of work is worth the 2-hour ADR investment, given this model's own risk assumptions. That's a genuinely useful, concrete threshold a team could actually apply - "would undoing this take more than about two work days?" - rather than a vague judgment call about whether a decision "feels important."