Independent solution

How to solve this Conditional Probability question

Setup

Setup

Convert the conditional probability of S given M into the joint probability of M and S.

Pr⁡(M∩S)=Pr⁡(S∣M)Pr⁡(M)=0.15(0.70)=0.105\Pr(M\cap S)=\Pr(S\mid M)\Pr(M)=0.15(0.70)=0.105

Model

Model

The probability of neither event is the complement of the union. Express it as one minus the two marginals plus their overlap.

Pr⁡(Mc∩Sc)=1−Pr⁡(M)−Pr⁡(S)+Pr⁡(M∩S)\Pr(M^c\cap S^c)=1-\Pr(M)-\Pr(S)+\Pr(M\cap S)

Compute

Compute

The overlap is 0.15(0.70)=0.105, so the probability of neither event is 1-0.70-0.20+0.105=0.205.

Pr⁡(Mc∩Sc)=1−0.70−0.20+0.105=0.205\Pr(M^c\cap S^c)=1-0.70-0.20+0.105=0.205

Answer

Answer

Rounding 0.205 to the precision of the choices gives 0.21, which is choice B.

0.21(B)\boxed{0.21\quad\text{(B)}}