Question

The probability that a certain beginner at golf gets good shot if he uses correct club is $\frac{1}{3},$ and the probability of a good shot with an incorrect club is $\frac{1}{4}.$ In his bag there are 5 different clubs only one of which is correct for the good shot. If he chooses a club at random and take a stroke, the probability that he gets a good shot is

• A. $\frac{1}{3}$
• B. $\frac{1}{12}$
• C. $\frac{4}{15}$
• D. $\frac{7}{12}$

Answer 1

The correct option is C $\frac{4}{15}$

P( getting correct club ) $=\frac{1}{5}$
Therefore P(hitting good shot by correct club) $=\frac{1}{3}\times \frac{1}{5}=\frac{1}{15}$
P(getting wrong club) $=\frac{4}{5}$
P(hitting good shot with wrong club) $=\frac{4}{5}\times \frac{1}{4}=\frac{1}{5}.$
Therefore P(hitting good shot) $=\frac{1}{15}+\frac{1}{5}=\frac{4}{15}.$