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
Answer and calculation
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.
0.80(D) 