The probability that a certain beginner at golf gets good shot if he uses correc

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

Options:

A . 13

B . 112

C . 415

D . 712

Answer: Option C
:
C
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} .

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