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 what is $P(B\cap C)$ equal to?

• A. $\frac{1}{12}$
• B. $\frac{3}{4}$
• C. $\frac{1}{15}$
• D. $\frac{1}{9}$

Answer 1

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

From the above drawn Venn diagram,

$P\left(B\right)=P(A\cap B\cap \overline{C})+P(\overline{A}\cap B\cap \overline{C})+P(B\cap C)$

$\therefore P(B\cap C)=P\left(B\right)-P(A\cap B\cap \overline{C})-P(\overline{A}\cap B\cap \overline{C})=\frac{3}{4}-\frac{1}{3}-\frac{1}{3}=\frac{1}{12}$