Question

Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. It is found that 10% of the members in that city prefer swimming on weekends and are female, while 55% of the members in that city prefer swimming on weekdays and are female.

The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is

Answer 1

40%

Explanation:

If we call by A the members that prefer swimming on weekends and by B the members that are women, we have that:

P(A) = 0.25

P(A and B) = 0.1

The probability of a member being female given that the person prefers swimming on weekends can be expressed as P(B|A) (that is, probability of B given A).

To find this value, we can use this formula:

P(B|A) = P(A and B) / P(A) = 0.25

So we have that:

P(B|A) = 0.1 / 0.25 = 0.4 = 40%