Question

Suppose 60% of homes in Miami have a swimming pool and 30% have both a swimming pool and a Jacuzzi. What is the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool?

Answer 1

0.5 is the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.

Explanation:

We are given the following in the question:

S: Homes in Miami have a swimming pool

J: Homes in Miami have a jacuzzi

`P(S) = 60\% = 0.6\\P(S\cap J) = 30\% = 0.3`

We have to find the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.

Thus, we have to calculation the conditional probability of having a jacuzzi given the house has a swimming pool.

`P(J|S) = (P(J\cap S))/(P(S))\\\\P(J|S) = \displaystyle(0.3)/(0.6) = 0.5`

0.5 is the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.