Question

If A and B are two events such that P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6, then find P(A|B).

Answer 1

As $P\left(B|A\right)=\frac{P(A\cap B)}{P\left(A\right)}\Rightarrow P(A\cap B)=P\left(B|A\right)P\left(A\right)=0.6\times 0.4=0.24$
$\therefore P\left(A|B\right)=\frac{P(A\cap B)}{P\left(B\right)}=\frac{0.24}{0.8}=0.3or\frac{3}{10}.$