P(A B)=34, P(A B)=14, P( A)=23.

Question

$P(A\cup B)=\dfrac34$, $P(A\cap B)=\dfrac14$, $P(\overline A)=\dfrac23$. Find $P(\overline A\cap B)$.

Accepted Answer

$P(A)=\dfrac13$. From $P(A\cup B)=P(A)+P(B)-P(A\cap B)$: $\dfrac34=\dfrac13+P(B)-\dfrac14 \Rightarrow P(B)=\dfrac23$.

$$P(\overline A\cap B) = P(B)-P(A\cap B) = \frac23-\frac14=\frac{5}{12}$$

Solutions · 1