in a subdivision, 67 perecent of the homes have detached garages, 32 perecent have a patio, and 13 percent have both. What is the probability that a house has a patio if you know that it has a detached garage?
would it be 32/67?
To find the probability that a house has a patio given that it has a detached garage, you can use the formula for conditional probability.
The formula for conditional probability is: P(A|B) = P(A and B) / P(B)
In this case, A represents having a patio and B represents having a detached garage.
Given that 67% of the homes have detached garages, you can say that P(B) = 0.67.
Given that 32% of the homes have a patio, you can say that P(A) = 0.32.
Given that 13% of the homes have both a detached garage and a patio, you can say that P(A and B) = 0.13.
Substituting these values into the formula, you get:
P(A|B) = P(A and B) / P(B) = 0.13 / 0.67
Therefore, the probability that a house has a patio given that it has a detached garage is indeed 0.13 / 0.67, which is approximately 0.194, or 19.4%.