This Exam P sample reference tests Conditional Probability. There are 625 records without the parental condition and 108 relevant deaths among them, giving 108/625=0.1728, choice B.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AThe value 0.115 is 108/937. It uses the full population as denominator instead of conditioning on the 625 records outside F.
CThe value 0.224 is 210/937, the unconditional proportion in H rather than Pr(H given F complement).
DThe value 0.327 is 102/312, the conditional proportion Pr(H given F); it conditions on F instead of its complement.
Original practice · fully worked
Original variant: infer a segment rate from the portfolio average
Forty percent of a portfolio consists of newly issued contracts, whose event rate is 0.12. The remaining contracts are seasoned. The whole portfolio has event rate 0.18. Determine the event rate among seasoned contracts.
A 0.120
B 0.180
C 0.220
D 0.240
E 0.300
Variant answer in brief
The portfolio rate is a two-segment weighted average. Solving 0.18=0.40(0.12)+0.60s gives s=0.22, choice C.
Setup
Setup
Let s be the event rate among seasoned contracts; the new and seasoned portfolio shares are 0.40 and 0.60.
s=Pr(E∣seasoned)
Model
Model
Express the overall event rate as the weighted average of the two segment-specific rates.
0.18=0.40(0.12)+0.60s
Compute
Compute
The new-contract contribution is 0.40(0.12)=0.048, leaving 0.132 for seasoned contracts; division by 0.60 gives s=0.22.
0.132=0.60s,s=0.22
Answer
Answer
The seasoned-contract event rate is 0.220, so the correct answer is choice C.
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