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Question

(C) Let $C$ be the event of choosing the correct club and $W$ be the event of choosing an incorrect club. Let $G$ be the event of getting a good shot.

Vedclass · Accepted Answer

$\frac{4}{15}$

Vedclass · Answer

(C) Let $C$ be the event of choosing the correct club and $W$ be the event of choosing an incorrect club. Let $G$ be the event of getting a good shot.Given:$P(C) = \frac{1}{5}$$P(W) = \frac{4}{5}$$P(G|C) = \frac{1}{3}$$P(G|W) = \frac{1}{4}$Using the Law of Total Probability:$P(G) = P(C) 	imes P(G|C) + P(W) 	imes P(G|W)$$P(G) = \left(\frac{1}{5} 	imes \frac{1}{3}ight) + \left(\frac{4}{5} 	imes \frac{1}{4}ight)$$P(G) = \frac{1}{15} + \frac{4}{20} = \frac{1}{15} + \frac{1}{5}$$P(G) = \frac{1 + 3}{15} = \frac{4}{15}$.

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