Question

If $P\left(A\right)=0.8,$ $P\left(B\right)=0.5$ and $P\left(\frac{B}{A}\right)=0.4$ then $P\left(\frac{A}{B}\right)=?$

• A. $0.32$
• B. $0.64$
• C. $0.16$
• D. $0.25$

Answer 1

The correct option is B $0.64$

$P\left(A\right)=0.8;P\left(B\right)=0.5$

$P\left(\frac{B}{A}\right)=0.4$

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

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

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

$\Rightarrow 1=\frac{0.8\times 0.4}{0.5\times P\left(A/B\right)}$

$\Rightarrow 0.5\times P\left(A/B\right)=0.32$

$P\left(A/B\right)=\frac{0.32}{0.5}\Rightarrow 0.64$