Question

In New York State, 38% of the houses have a pool and 21% of the houses have both a pool and a hot tub. What is the probability that a

house has a hot tub given that it has a pool?
O 8%
O 55%
O 108%
O 59%​

Answer 1

Probability that a house has a hot tub given that it has a pool is 55%.

Explanation:

We are given that in New York State, 38% of the houses have a pool and 21% of the houses have both a pool and a hot tub.

Let the probability that houses have a pool = P(A) = 0.38

Also, let B = event that houses have a hot tub

Probability that houses have both a pool and a hot tub =
`P(A \bigcap B)` = 0.21

Now, the conditional probability that a house has a hot tub given that it has a pool is given by = P(B / A)

As we know that; P(B / A) =
`(P(A \bigcap B))/(P(A) )`

=
`(0.21)/(0.38)`

= 0.553 ≈ 55%

Hence, the probability that a house has a hot tub given that it has a pool is 55%.