The probabilities of two persons to hit a tar | vedclass

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Question

(C) Let $P(A)$ be the probability that the first person hits the target and $P(B)$ be the probability that the second person hits the target. Given $P

Vedclass · Accepted Answer

$\frac{2}{5}$

Vedclass · Answer

(C) Let $P(A)$ be the probability that the first person hits the target and $P(B)$ be the probability that the second person hits the target. Given $P(A) = \frac{1}{4}$ and $P(B) = \frac{1}{5}$. The target is hit if at least one of them hits the target. It is easier to calculate the probability that the target is not hit at all. The probability that the first person misses is $P(A') = 1 - P(A) = 1 - \frac{1}{4} = \frac{3}{4}$. The probability that the second person misses is $P(B') = 1 - P(B) = 1 - \frac{1}{5} = \frac{4}{5}$. Since they attempt independently, the probability that both miss is $P(A' \cap B') = P(A') 	imes P(B') = \frac{3}{4} 	imes \frac{4}{5} = \frac{3}{5}$. The probability that the target is hit is $1 - P(A' \cap B') = 1 - \frac{3}{5} = \frac{2}{5}$. Thus, the correct option is $C$.

The probabilities of two persons to hit a target are $\frac{1}{4}$ and $\frac{1}{5}$ respectively. The probability that the target is being hit when both of them attempt independently is

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