When a missile is fired from a ship,the proba | vedclass

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(C) Let $I$ be the event that the missile is intercepted and $H$ be the event that the missile hits the target. Given: $P(I) = \frac{1}{3}$,so $P(	ex

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$\frac{1}{8}$

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(C) Let $I$ be the event that the missile is intercepted and $H$ be the event that the missile hits the target. Given: $P(I) = \frac{1}{3}$,so $P(	ext{not intercepted}) = P(I^c) = 1 - \frac{1}{3} = \frac{2}{3}$. The probability that the missile hits the target given it is not intercepted is $P(H | I^c) = \frac{3}{4}$. The probability that a single missile hits the target is $P(H) = P(I^c) 	imes P(H | I^c) = \frac{2}{3} 	imes \frac{3}{4} = \frac{1}{2}$. Since three missiles are fired independently,the probability that all three hit the target is $(P(H))^3 = (\frac{1}{2})^3 = \frac{1}{8}$.

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