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

Option: D is the correct answer.

                 D) 0.40

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:

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:

( 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 )   )