This Exam P sample reference tests Expected Value. The mutually exclusive policy groups have weights 0.50, 0.35, and 0.15; their renewal-weighted sum is 0.53, choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AThe value 20% is only the contribution 0.40(0.50) from the A-only group and omits the other two groups.
CThe value 41% is 0.20+0.21, which omits the 0.80(0.15)=0.12 contribution from policyholders with both coverages.
Original practice · fully worked
Original variant: recover one tier's renewal rate
A publisher assigns 46 of every 100 subscribers to Basic service, 34 to Plus, and the remainder to Pro. Basic and Plus renewal rates are 0.42 and 0.68. Across all tiers, the renewal rate is 0.6004. Determine the Pro renewal rate.
A 0.6004
B 0.6800
C 0.7600
D 0.8800
E 0.9200
Variant answer in brief
After removing the Basic and Plus contributions, the remaining renewal mass is 0.176. Dividing by the Pro share 0.20 gives 0.88, choice D.
Setup
Setup
Let r be the Pro renewal rate. The Pro share is the remaining 1-0.46-0.34=0.20 of subscribers.
0.6004=0.46(0.42)+0.34(0.68)+0.20r
Model
Model
Write the overall renewal rate as the weighted average of the Basic, Plus, and Pro rates.
0.20r=0.6004−0.1932−0.2312=0.1760
Compute
Compute
After subtracting the Basic and Plus contributions from 0.6004, the Pro tier contributes 0.1760; dividing by its 0.20 share gives r=0.88.
r=0.1760/0.20=0.88
Answer
Answer
The Pro renewal rate is therefore 0.8800, which is choice D.
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