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

Answer:

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

Step-by-step 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)  =  $\frac{P(A \bigcap B)}{P(A) }$

                                              =  $\frac{0.21}{0.38}$  

                                              =  0.553 ≈ 55%

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