Question

If $P\left(B\right)=\frac{3}{4},P(A\cap B\cap \overline{C})=\frac{1}{3}$ and $P(\overline{A}\cap B\cap \overline{C})=\frac{1}{3}$ then $P(B\cap C)$ is

• A. $\frac{1}{12}$
• B. $\frac{1}{6}$
• C. $\frac{1}{15}$
• D. $\frac{1}{5}$

Answer 1

The correct option is A $\frac{1}{12}$

$P(B\cap C)=P\left(B\right)-\{P(A\cap B\cap C^c)+P(A^c\cap B\cap C^c)\}$
$\Rightarrow P(B\cap C)=\frac{3}{4}-\{\frac{1}{3}+\frac{1}{3}\}$
$\Rightarrow P(B\cap C)=\frac{1}{12}$