If P(A)=13, P(B)=15, P(A B)=12, find P(A B')+P(B A').

Question

If $P(A)=\dfrac13$, $P(B)=\dfrac15$, $P(A\cup B)=\dfrac12$, find $P(A\mid B')+P(B\mid A')$.

Accepted Answer

$$P(A\cap B) = \frac13+\frac15-\frac12=\frac{1}{30}$$

$$P(A\mid B')+P(B\mid A') = \frac{P(A)-P(A\cap B)}{1-P(B)}+\frac{P(B)-P(A\cap B)}{1-P(A)} = \frac{9/30}{4/5}+\frac{5/30}{2/3}=\frac58$$

Solutions · 1