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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.

Correct Answer: 3/20

Explanation:

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


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