Question

If $A$ and $B$ are two events such that $P\left(A\right)=0.3,P\left(B\right)=0.6$ and $P\left(B/A\right)=0.5$ then $P\left(A/B\right)$=

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C $\frac{1}{4}$

$P\left(A\right)=0.3P\left(B\right)=0.6$

$P\left(B/A\right)=0.5=\frac{P(A\cap B)}{P\left(A\right)}$

$P(A\cap B)=0.5\times P\left(A\right)=0.15$

$P\left(A/B\right)=\frac{P(A\cap B)}{P\left(B\right)}=\frac{0.15}{0.6}=0.25=\frac{1}{4}$