In a subdivison, 67% of homes have detached garages, 32% have a patio, and 13% have both. What is the probability that a house has a pation if you know that it has a detached garage? Please explain how you did the work, thanks.
"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%.
a class of 14 girls and 15 boys if all of their name are put on separate slips in a hat what is the probsbility of each person name being drawed
To find the probability that a house has a patio if you know it has a detached garage, you can use the concept of conditional probability.
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%.