A can hit a target 4 times in 5 shots,B can h | vedclass

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(C) Let $P(A)$,$P(B)$,and $P(C)$ be the probabilities of hitting the target for $A$,$B$,and $C$ respectively.$P(A) = \frac{4}{5}$,$P(A') = \frac{1}{5}

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$\frac{5}{6}$

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(C) Let $P(A)$,$P(B)$,and $P(C)$ be the probabilities of hitting the target for $A$,$B$,and $C$ respectively.$P(A) = \frac{4}{5}$,$P(A') = \frac{1}{5}$$P(B) = \frac{3}{4}$,$P(B') = \frac{1}{4}$$P(C) = \frac{2}{3}$,$P(C') = \frac{1}{3}$'At least two shots hit' means either exactly two hit or all three hit.Probability = $P(A \cap B \cap C') + P(A \cap B' \cap C) + P(A' \cap B \cap C) + P(A \cap B \cap C)$$= (\frac{4}{5} 	imes \frac{3}{4} 	imes \frac{1}{3}) + (\frac{4}{5} 	imes \frac{1}{4} 	imes \frac{2}{3}) + (\frac{1}{5} 	imes \frac{3}{4} 	imes \frac{2}{3}) + (\frac{4}{5} 	imes \frac{3}{4} 	imes \frac{2}{3})$$= \frac{12}{60} + \frac{8}{60} + \frac{6}{60} + \frac{24}{60} = \frac{50}{60} = \frac{5}{6}$

$A$ can hit a target $4$ times in $5$ shots,$B$ can hit a target $3$ times in $4$ shots,and $C$ can hit a target $2$ times in $3$ shots. All three fire a shot each. What is the probability that at least two shots hit the target?

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