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In a small town 50% of 2 story homes own computers and 35% of one story homes own computers. In dawn's neighborhood 75% of homes are 2 story. What is the probability that a two story home in dawn's neighborhood owns a computer

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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.

User Mustafa ALMulla
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