Question

If $P\left(X\right)=\frac{1}{2};P\left(Y\right)=\frac{1}{3}andP\left(X/Y\right)=\frac{1}{3}thenP(X\cap Y)$ is

• A. $\frac{1}{6}$
• B. $\frac{1}{9}$
• C. $\frac{1}{12}$
• D. $\frac{1}{18}$

Answer 1

The correct option is B $\frac{1}{9}$

Since, $P\left(\frac{X}{Y}\right)=\frac{P(X\cap Y)}{P\left(Y\right)}$


$\Rightarrow P(X\cap Y)=P\left(\frac{X}{Y}\right).P\left(Y\right)=\frac{1}{3}\times \frac{1}{3}=\frac{1}{9}$