Question

Probability of $A$ to hit a target is $\frac{1}{4}$. Probability of $B$ to hit a target is $\frac{1}{3}$. If $A$ and $B$ are

independent event what is the probability of $A$ to hit a target given that the target is hit?

Answer 1

P(target is hit once)=P(A hitting).P(B not hitting)+P(A not hitting).P(B hitting)

$\begin{array}{c}=\frac{1}{4}.\frac{2}{3}+\frac{3}{4}.\frac{1}{3}\\ =\frac{5}{12}\end{array}$

$P\left(Ahitting/targetishitonce\right)=\frac{P\left(Ahitting\right).P\left(Bnothitting\right)}{P\left(targetishitonce\right)}=\frac{\frac{1}{6}}{\frac{5}{12}}=\frac{2}{5}$