Help please (Proability)

Question

A fitness club has 100 members.

In a survey, the tness club nds that

18 of the members use the gym and the swimming pool. 54 members use the gym.

12 members do not use the gym or the swimming pool.

Two members from the club are selected at random.

Given that both members use the swimming pool,

work out the probability that both members also use the gym.

5 MARKS

Answer 1

Not sure about the answer, but I am thinking along these lines ===>

1. Since 12 of the 100 members dont use either gym or swimming pool, the set of member who use the services becomes 88.
2. Since 54 members use gym and 18 member use gym & swimming, these people grouped together form 54 + 18 = 72 members. Therefore remaining of 88 members who do only swimming are 16. (88 - 72)
3. Given 2 members selected who definitely do swimming, the 2 so chosen would be out of the 18 members. So, total number of people who do swimming only and gym-swimming become (16+18) = 34.
4. Then the probability of these 2 also doing swimming could be (18/34) = 9/17