Based on published real estate research, 65% of homes for sale have garages, 20% have swimming pools, and 18% have both features.
i. Given that a home for sale has a garage, what’s the probability that it also has a pool
I get .27 but that's not an answer choice.
.65 * .20 = ?
To find the probability that a home with a garage also has a pool, we can use conditional probability.
Conditional probability is the likelihood of an event happening given that another event has already occurred. In this case, we are looking for the probability that a home has a pool, given the condition that it already has a garage.
Let's use the formula for conditional probability:
P(A|B) = P(A ∩ B) / P(B)
Where:
- P(A|B) represents the probability of event A happening given that event B has occurred.
- P(A ∩ B) represents the probability of both events A and B happening.
- P(B) represents the probability of event B happening.
Given the information provided:
- P(A ∩ B) = 18% (the percentage of homes that have both a garage and a pool)
- P(A) = 65% (the percentage of homes that have a garage)
- P(B) = ? (the probability we want to find, which is the likelihood of a home having a pool given that it has a garage)
Now, substituting the values into the formula:
P(A|B) = P(A ∩ B) / P(B)
P(A|B) = 18% / 65%
Therefore, the probability that a home with a garage also has a pool is 18% divided by 65%.