Independent solution

How to solve this Set Probability question

Setup

Setup

Partition clients outside auto coverage into homeowners-only, renters-only, and neither. The supplied percentages determine each of these disjoint cells.

P(Ac)=0.36P(A^c)=0.36
P(none)=0.17P(\text{none})=0.17
P(H∩Ac)=0.11P(H\cap A^c)=0.11

Model

Model

Subtract the neither and homeowners-only cells from the 36% without auto to obtain 8% renters-only. Let total homeowners coverage be twice total renters coverage.

P(R∩Ac)=0.36−0.17−0.11=0.08P(R\cap A^c)=0.36-0.17-0.11=0.08
H=2RH=2R

Compute

Compute

Express the two auto intersections by subtracting the known non-auto cells from their coverage totals. The 35% double-coverage condition gives total renters coverage 18%.

(H−0.11)+(R−0.08)=0.35(H-0.11)+(R-0.08)=0.35
3R=0.543R=0.54
R=0.18R=0.18
P(A∩R)=0.18−0.08=0.10P(A\cap R)=0.18-0.08=0.10

Answer

Answer

Subtracting the 8% renters-only cell leaves 10% with both auto and renters coverage, choice B.

10%(B)\boxed{10\%\quad\text{(B)}}