Question

The probability that a certain beginner at golf gets a good shot if he uses the correct club is $\frac{1}{3},$ and the probability of a good shot with an incorrect club is $\frac{1}{4}.$ In his bag are $5$ different clubs, only one of which is correct for the shot in question. If he chooses a club is correct for the shot in question. If he chooses a club at random and takes a stroke, the probability that he get 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 this 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$)=\frac{1}{15}+\frac{1}{5}=\frac{4}{15}$