Real Estate ads suggest that 50% of homes for sale have garages, 24% have swimming pools, and 11% have both. If a home for sale has a garage, what's the probability that it has a pool too? Write as a decimal.

Conditional probability.

P=pool
G=garage
Probability of a home having a pool given that it has a garage is
P(P|G)=P(P∩G)/P(G)
=11%/50%
=22%

45

To solve this problem, we can use conditional probability. Let's denote the event of a home having a garage as G and the event of a home having a swimming pool as P.

We are given that 50% of homes for sale have garages (P(G) = 0.5), 24% have swimming pools (P(P) = 0.24), and 11% have both (P(G ∩ P) = 0.11).

We want to find the probability that a home with a garage also has a swimming pool, which can be written as P(P|G).

By using the formula for conditional probability, we have:

P(P|G) = P(G ∩ P) / P(G)

Substituting the given values, we get:

P(P|G) = 0.11 / 0.5

Simplifying, we find:

P(P|G) = 0.22

Therefore, the probability that a home with a garage also has a swimming pool is 0.22.

To find the probability that a home for sale has a pool given that it has a garage, we need to use conditional probability. In this case, we are looking for the probability of a home having both a garage and a pool, given that it has a garage.

Let's denote:
A = Home has a garage
B = Home has a pool

We are given the following information:
P(A) = 0.50 (50% of homes have garages)
P(B) = 0.24 (24% of homes have pools)
P(A ∩ B) = 0.11 (11% of homes have both a garage and a pool)

The formula for conditional probability is:
P(B|A) = P(A ∩ B) / P(A)

Now let's substitute the values into the formula:
P(B|A) = 0.11 / 0.50

Calculating the division, we find that the probability is:
P(B|A) = 0.22

Therefore, the probability that a home for sale has a pool given that it has a garage is 0.22 (or 22% as a decimal).