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Question
The probability that A hits the target is `1/3` and the probability that B hits it, is `2/5`. If both try to hit the target independently, find the probability that the target is hit.
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Solution
P(A) = P(A hits target) = `1/3`
P(B) = P(B hits target) = `2/5`
Now, P(A ∪ B) = P(target will be hit)
= P(A) + P(B) – P(A ∩ B)
= P(A) + P(B) – P(A).P(B) ...[∵ A and Bare independent]
= `1/3 + 2/5 - 1/3 xx 2/5`
= `(5 + 6 - 2)/15`
= `9/15`
= `3/5`
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