The odds favouring the event of a person hitting a target are 3 to 5. The odds against the event of another person hitting the target are 3 to 2. If each of them fire once at the target, find the probability that both of them hit the target.

Let A be the event of first person hitting the target,

$P\left(A\right) =\frac{3}{3+5}=\frac{3}{8} (odd in favour)$

Let B be the event of Second person hitting a target.

$P\left(B\right)=\frac{2}{3+2}=\frac{2}{5} (odd against)$

Since both events are independent and both will hit the target so,

$P(A\cap B)= P\left(A\right)P\left(B\right)=\frac{3}{8}\times \frac{2}{5}=\frac{3}{20}$