Question

Of the homes on the market, 38% have pools, 70% have at least 3 bedrooms, and 25% have both a pool and at least 3 bedrooms. If a home is chosen at random, what is the probability that it has a pool, given it has at least 3 bedrooms?

Answer 1

Therefore,

P(A|B) = P(A and B) / P(B) = 0.25 / 0.70 ≈ 0.357

So the probability that a home has a pool, given that it has at least 3 bedrooms, is approximately 0.357 or 35.7%.

Explanation:

We are given that 38% of the homes have pools, 70% have at least 3 bedrooms, and 25% have both a pool and at least 3 bedrooms.

We are asked to find the probability that a home has a pool, given that it has at least 3 bedrooms. Let P(A) represent the probability of a home having a pool, and P(B) represent the probability of a home having at least 3 bedrooms. We need to find P(A|B), the conditional probability of a home having a pool given that it has at least 3 bedrooms.

Using Bayes' theorem, we have:

P(A|B) = P(A and B) / P(B)

We are given that 25% of the homes have both a pool and at least 3 bedrooms, which means that P(A and B) = 0.25. We are also given that 70% of the homes have at least 3 bedrooms, which means that P(B) = 0.70.

Answer 2

Let P be the event that a home has a pool, and B be the event that a home has at least 3 bedrooms. We want to find P(P|B), the probability that a home has a pool given that it has at least 3 bedrooms.

By Bayes' theorem, we have:

P(P|B) = P(B|P) * P(P) / P(B)

We are given:

P(P) = 0.38, the probability that a home has a pool

P(B) = 0.70, the probability that a home has at least 3 bedrooms

P(P and B) = 0.25, the probability that a home has both a pool and at least 3 bedrooms

To find P(B|P), the probability that a home has at least 3 bedrooms given that it has a pool, we use the conditional probability formula:

P(B|P) = P(B and P) / P(P)

We know P(B and P) = P(P and B) = 0.25, and P(P) = 0.38, so:

P(B|P) = 0.25 / 0.38 = 0.6579 (rounded to four decimal places)

Now we can use Bayes' theorem to find P(P|B):

P(P|B) = P(B|P) * P(P) / P(B)

= 0.6579 * 0.38 / 0.70

= 0.3555 (rounded to four decimal places)

Therefore, the probability that a home has a pool given that it has at least 3 bedrooms is approximately 0.3555.