Let E and F are events associated with an experiment. If $P(E)= 0.4, P(F) = 0.8$ and $P(F|E) = 0.6$, then $P(E|F)$ is

0.3

The correct answer is Option (3) → 0.3

$P(E)=0.4$

$P(F)=0.8$

$P(F|E)=0.6$

$P(F|E)=\frac{P(E\cap F)}{P(E)}$

$0.6=\frac{P(E\cap F)}{0.4}$

$P(E\cap F)=0.6\times0.4$

$P(E\cap F)=0.24$

Now,

$P(E|F)=\frac{P(E\cap F)}{P(F)}$

$=\frac{0.24}{0.8}$

$=\frac{24}{80}$

$=\frac{3}{10}$

$P(E|F)=\frac{3}{10}$