Question

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

• A. $\frac{1}{12}$
• B. $\frac{1}{6}$
• C. $\frac{1}{15}$
• D. $\frac{1}{9}$

Answer 1

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

$P\left(B\right)=\frac{3}{4},P(A\cap B\cap \overline{C})=\frac{1}{3}$ and $P(\overline{A}\cap B\cap \overline{C})=\frac{1}{3}$
Therefore from venn diagram
$P(B\cap C)=P\left(B\right)-(P(A\cap B\cap \overline{C})+P(\overline{A}\cap B\cap \overline{C}))$

$=\frac{3}{4}-(\frac{1}{3}+\frac{1}{3})=\frac{3}{4}-\frac{2}{3}=\frac{1}{12}$