Question

If A and B are two independent events such that $P(\overline{A}\cap B)=\frac{2}{15}$ and $P(A\cap \overline{B})=\frac{1}{6}$, then P(B) is

• A. $\frac{1}{5}$
• B. $\frac{1}{6}$
• C. $\frac{2}{5}$
• D. $\frac{5}{6}$

Answer 1

The correct option is B $\frac{1}{6}$

$P(\overline{A}\cap B)=\frac{2}{15}\Rightarrow (1-P(A\left)\right)P\left(B\right)=\frac{2}{15}\dots \dots \left(i\right)P(A\cap \overline{B})=\frac{1}{6}\Rightarrow P\left(A\right)(1-P(B\left)\right)=\frac{1}{6}\dots \dots \left(ii\right)$
From (i) and (ii) solving for P(B)
We get, $P\left(B\right)=\frac{1}{6}$