Question

Calculate $P\left(B/A\right)$ if $P\left(A/B\right)=0.25,P\left(A\right)=0.4$ and $P\left(B\right)=0.5$.

• A. $0.5325$
• B. $0.3125$
• C. $0.4125$
• D. None of these

Answer 1

Answer: (B)

$0.3125$

Given $P\left(A/B\right)=0.25,P\left(A\right)=0.4,P\left(B\right)=0.5$

We have to find $P\left(B/A\right)$.

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

$\Rightarrow P(A\cap B)=P\left(A/B\right)\times P\left(B\right)$

$=0.25\times 0.5$

$P(A\cap B)=0.125$

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

$=\frac{0.125}{0.4}$

$P\left(B/A\right)=0.3125$