This Exam P sample reference tests Bayes’ Theorem. Young adults contribute 0.0128 to collision probability; all four groups contribute 0.0583, so the posterior is 0.21955, choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AThe value 0.06 is the total collision probability 0.0583 rounded, not the posterior age-group probability.
BThe value 0.16 is the prior young-adult population share before collision rates are applied.
Original practice · fully worked
Original variant: posterior within two eligible campaign segments
A campaign sends 25% of traffic to segment B and 25% to segment D. Segment B fails on eight visits per hundred, while segment D fails on two per hundred. A failed conversion is known to have come from one of these two segments. Find the probability that it came from B.
A 0.20
B 0.25
C 0.50
D 0.80
E 0.90
Variant answer in brief
The two eligible failure weights are 0.020 and 0.005. Segment B supplies four fifths of the restricted evidence, choice D.
Setup
Setup
Within the stated two-segment restriction, compute each segment's joint failure weight from its traffic share and failure rate.
wB=0.25(0.08)=0.020
wD=0.25(0.02)=0.005
Model
Model
Condition on both failure and membership in the two eligible segments by normalizing the segment-B weight over the two weights.
Pr(B∣F,B∪D)=wB+wDwB
Compute
Compute
The eligible failure weights are 0.020 and 0.005, so segment B contributes 0.020/0.025=0.80 of the restricted evidence.
Pr(B∣F,B∪D)=0.020/0.025=0.80
Answer
Answer
The failed conversion came from segment B with probability 0.80, which is choice D.
The 3108-page Probability Proof Manual reorganizes 718 verified Exam P solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
