Question

An individual is picked at random from a group of 52 athletes.Suppose that 26 athletes are female of whuch 6 are swimmers.Also there are 10 seimmers among male athletes.
1.Given that the individual picked at random is female,find the probability that she is a swimmer.
2.Given that the individual picked us a swimmer ,find the probability that he is a male

Answer 1

Answer to Question #84159 – Math – Statistics and Probability

Let event M = ‘an individual athlete is male’;

F = ‘an individual athlete is female’;

S = ‘an individual athlete is swimmer’.

Given total number of athletes = 52,

total number of female athletes = 26,

total number of male athletes = 26,

number of female swimmer athletes = 6,

number of male swimmer athletes = 10,

hence total number of swimmer athletes = 10 + 6 = 16.

1. We need P(S / F)

$$P(S / F) = \frac{P(S \cap F)}{P(F)} = \frac{6 / 52}{26 / 52} = \frac{6}{26} = \frac{3}{13}$$

2. We need P(M/S)

$$P(M / S) = \frac{P(M \cap S)}{P(S)} = \frac{10 / 52}{16 / 52} = \frac{10}{16} = \frac{5}{8}$$

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