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
Solution
Correct Answer: Option D
Let A be the event of first person hitting the target,
\(P(A)\;=\frac3{3+5}=\frac38\;\;(odd\;in\;favour)\)
Let B be the event of Second person hitting a target.
\(P(B)=\frac2{3+2}=\frac25\;(odd\;against)\)
Since both events are independent and both will hit the target so,
\(P(A\cap B)=\;P(A)P(B)=\frac38\times\frac25=\frac3{20}\)
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