Question

Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. 10% of the members in the city prefer swimming on weekends and are female. 55% of the members in the city prefer swimming on weekdays and are female. What is the probability that a randomly selected club member is female, given that the person prefers swimming on weekends? (A).19, (B).20, (C).24, (D).40, (E).55

Answer 1

Option: D is the correct answer.

D) 0.40

Step-by-step explanation:

Let A denote the event that the person is female.

B denote the event that the person goes to swimming on weekends.

let P denote the probability of an event.

We are asked to find the probability:

P(A|B)

We know that:

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

Where A∩B denote the probability that the person is female and goes to swimming on Weekend.

Now from the given information we have:

Hence, we have:

`P(A|B)=(0.10)/(0.25)\\\\\\P(A|B)=0.40`

( since P(A∩B)=0.10 as 10% of the members in the city prefer swimming on weekends and are female .

P(B)=0.25 ( Since, 25% prefer swimming on weekends ) )

Answer 2

10% of the 25% of people that prefer to swim on weekends are female.

Multiply 10% and 25% to get 0.025

55% of the 75% are females who prefer to swim on the weekdays.
Multiply them together getting 0.4125

Divide 0.25 by 0.10= 0.40