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 ( A ) = 3 3 + 5 = 3 8 ( o d d i n f a v o u r )

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

P ( B ) = 2 3 + 2 = 2 5 ( o d d a g a i n s t )

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

P ( A ? B ) = P ( A ) P ( B ) = 3 8 × 2 5 = 3 20