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, there are $5$different clubs, only one of which is correct for the shot in question. If he chooses a club at random and takes a stroke, the probability that he gets a good shot is

The correct option is C

$\frac{4}{15}$

The explanation for the correct answer.

Solve for the probability of a good shot.

The probability of the correct club $=\frac{1}{5}$

Hence, the probability of hitting a good shot by using the correct club $=\left(\frac{1}{3}\right)\times \left(\frac{1}{5}\right)=\frac{1}{15}$

The probability of an incorrect club $=\frac{4}{5}$

Hence, the probability of hitting a good shot by using an incorrect club $=\left(\frac{1}{4}\right)\times \left(\frac{4}{5}\right)=\frac{1}{5}=\left(\frac{1}{4}\right)\times \left(\frac{4}{5}\right)=\frac{1}{5}$

Therefore, the probability of hitting a good shot $=\left(\frac{1}{15}\right)+\left(\frac{1}{15}\right)$

$$\begin{gathered} =\frac{1+3}{15} \\ =\frac{4}{15} \end{gathered}$$

Hence, option(C) is the correct answer.