"What is the probability that a house has a pation if you know that it has a detached garage?"
You're looking at the probability of a house that has both, therefore 13%.
You're looking at the probability of a house that has both, therefore 13%.
Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, the event A is having a patio, and the event B is having a detached garage.
The formula for conditional probability is:
P(A|B) = P(A∩B) / P(B)
Where P(A|B) is the probability of event A occurring given that event B has occurred,
P(A∩B) is the probability of both events A and B occurring,
and P(B) is the probability of event B occurring.
Given that 67% of homes have detached garages and 13% have both, we can conclude that the probability of having just a detached garage is 67% - 13%, which is 54%.
Now we can calculate the probability of having a patio if you know it has a detached garage using the formula.
P(A|B) = P(A∩B) / P(B)
In this case, A is having a patio, and B is having a detached garage.
P(A|B) = 13% / 54% = 0.24 ≈ 24%
Therefore, the probability that a house has a patio if you know it has a detached garage is approximately 24%.