To solve this problem, we can use Bayes' theorem. Let's define:
- A: two story home
- B: owning a computer
We want to find the probability of B given A, which we can write as P(B|A). Using Bayes' theorem, we have:
P(B|A) = P(A|B) * P(B) / P(A)
We know that 50% of two story homes own computers, so P(B) = 0.5. We also know that 75% of homes in Dawn's neighborhood are two story, so P(A) = 0.75.
To find P(A|B), we need to use the conditional probability formula:
P(A|B) = P(A and B) / P(B)
We don't have the probabilities for A and B happening together, but we know that:
P(A and B) = P(B|A) * P(A)
Substituting this into the conditional probability formula gives:
P(A|B) = (P(B|A) * P(A)) / P(B)
Putting all the values together, we get:
P(B|A) = (P(A|B) * P(B)) / P(A)
= ((P(B|A) * P(A)) / P(B)) * P(B) / P(A)
= (P(B and A) / P(B)) * P(B) / P(A)
= P(A and B) / P(B)
Substituting the values gives:
P(B|A) = (0.5 * 0.75) / 0.5
= 0.75
Therefore, the probability that a two story home in Dawn's neighborhood owns a computer is 0.75.