Two planes I and II drop bombs on a target. T | vedclass

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Question

(A) Let $A$ be the event that plane $I$ hits the target and $B$ be the event that plane $II$ hits the target.Given: $P(A) = 0.3$,so $P(A^c) = 1 - 0.3

Vedclass · Accepted Answer

$0.14$

Vedclass · Answer

(A) Let $A$ be the event that plane $I$ hits the target and $B$ be the event that plane $II$ hits the target.Given: $P(A) = 0.3$,so $P(A^c) = 1 - 0.3 = 0.7$.Given: $P(B) = 0.2$.The second plane drops the bomb only if the first plane fails to hit the target.This means we need to find the probability that the first plane fails $AND$ the second plane hits the target.Since these are independent events,the required probability is $P(A^c \cap B) = P(A^c) 	imes P(B)$.Substituting the values: $0.7 	imes 0.2 = 0.14$.Therefore,the probability that the second plane hits the target is $0.14$.

Two planes $I$ and $II$ drop bombs on a target. The probabilities of hitting the target by $I$ and $II$ are $0.3$ and $0.2$ respectively. The second plane drops the bomb only if the first plane fails to hit the target. What is the probability that the second plane hits the target?

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