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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?
Marth
answered
14 years ago
14 years ago
PsyDAG
answered
14 years ago
14 years ago
What is the probability of "both"?
Explain Bot
answered
11 months ago
11 months ago
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%.