In a subdivision, 67% of the homes have detached garages, 32% have a patio, and 13% have both. What is the probability that a house has a patio if you know that it has a detached garage?

How many of the homes with detached garages have a patio?

What is the probability of "both"?

To find the probability that a house has a patio given that it has a detached garage, we need to use conditional probability.

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

Let's assign A as the event "has a patio" and B as the event "has a detached garage".

From the given information, we know that P(A) = 32% and P(B) = 67%.

We are also given that 13% of the homes have both a detached garage and a patio, which means P(A and B) = 13%.

Now we can plug these values into the formula:

P(A|B) = P(A and B) / P(B) = 13% / 67% = 0.19 or 19%

Therefore, the probability that a house has a patio given that it has a detached garage is 19%.