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 20% 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_____.
P = Desired outcomes divided by the total outcomesm me

Answer 1

The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is 0.8 = 80%.

Explanation:

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Prefers swimming on weekends.

Event B: Being female.

25% prefer swimming on weekends

This means that
`P(A) = 0.25`

It is found that 20% of the members in that city prefer swimming on weekends and are female

This means that
`P(A \cap B) = 0.2`

So

`P(B|A) = (P(A \cap B))/(P(A)) = (0.2)/(0.25) = 0.8`

The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is 0.8 = 80%.