Question

It is given that event A & B are such that $P\left(A\right)=\frac{1}{4},P\left(\frac{A}{B}\right)=\frac{1}{2},P\left(\frac{B}{A}\right)=\frac{2}{3},$ then $P\left(B\right)=$

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{1}{2}$
• D. $\frac{1}{6}$

Answer 1

Answer: (A)

$\frac{1}{3}$

We have that $P\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P\left(B\right)}$

$=\frac{P(A\cap B)}{P\left(A\right)}\times \frac{P\left(A\right)}{P\left(B\right)}$

$\Rightarrow P\left(\frac{A}{B}\right)=P\left(\frac{B}{A}\right)\cdot \frac{P\left(A\right)}{P\left(B\right)}$

$\therefore P\left(B\right)=\frac{2/3\times 1/4}{1/2}=\frac{1}{3}$