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.

Answer 1

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`