Question

Find $P\left(B/A\right)$ when $P\left(A\right)=\frac{5}{11},P\left(B\right)=\frac{6}{11}$ and $P(A\cup B)=\frac{7}{11}$.

Answer 1

Given:-

$P\left(A\right)=\frac{5}{11}$

$P\left(B\right)=\frac{6}{11}$

$P(A\cup B)=\frac{7}{11}$

To find:- $P\left(B/A\right)=?$

As we know that,

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$\therefore \frac{7}{11}=\frac{5}{11}+\frac{6}{11}-P(A\cap B)$

$P(A\cap B)=\frac{5}{11}+\frac{6}{11}-\frac{7}{11}=\frac{5+6-7}{11}=\frac{4}{11}$

$\therefore P\left(B/A\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{\left(\frac{4}{11}\right)}{\left(\frac{5}{11}\right)}$

$\Rightarrow P\left(B/A\right)=\frac{4}{5}$