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all a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated. According to a survey, P(A) = 0.137, P(B) = 0.272, and the probability that a household is both prosperous and educated is P(A and B) = 0.082. What is the conditional probability that a household is prosperous, given that it is educated? (Round your answer to four decimal places.)

Respuesta :

Answer:

A= the event that the selected household is prosperous

B= the event that the selected household is educated

[tex] P(A) =0.137, P(B) =0.272, P(A \cap B) =0.082[/tex]

[tex]P(A|B)= \frac{0.082}{0.272}= 0.3015[/tex]

And that represent the final answer for this case.

Step-by-step explanation:

For this case we define the following events:

A= the event that the selected household is prosperous

B= the event that the selected household is educated

We have the following probabilities given:

[tex] P(A) =0.137, P(B) =0.272, P(A \cap B) =0.082[/tex]

For this case we want to calculate the conditional probability that a household is prosperous, given that it is educated.

So this probability can be expressed as [tex] P(A|B) [/tex]

Using the Bayes rule we know that:

[tex] P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]

And for this case we have everything in order to replace, and we got:

[tex]P(A|B)= \frac{0.082}{0.272}= 0.3015[/tex]

And that represent the final answer for this case.