Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 38 / 4 / c / Solution

The first 12 weeks are in custody and carry no stated overdose deaths. Thus the 26-week sentence-based window includes 14 weeks after release: the first two weeks followed by the next twelve. Interpreting the later probability conditionally on surviving the earlier interval givesHenceIf the two quoted frequencies instead use the same original cohort as their denominator, add the two marginal probabilities to get exactly 90 expected deaths. The conditional-survival calculation makes the denominator interpretation explicit; both conventions agree at the rounded precision of the quoted rates.