4.70 Education and income. Call a household prosperous if its income exceeds $10

Question

4.70 Education and income. Call a household prosperous if its income exceeds $100,000. Call the household educated if at least one of the householders completed college. Select an American household at ran dom, and let A be the event that the selected household is prosperous and B the event that it is educated. According to the Current Population Survey, P(A) 0.138, P(B) = 0.261, and the probability that a household is both pros- perous and educated is P(A and B) = 0.082. What is the probability P(A or B) that the household selected is either prosperous or educated?

Explanation / Answer

Given that,

Let A be the event that the selected household is prosperous.

B be the event that it is educated.

P(A) = 0.138

P(B) = 0.261

P(A and B) = 0.082

And we have to find P(A or B).

By using addition rule of probability,

P(A or B) = P(A) + P(B) - P(A and B)

= 0.138 + 0.261 - 0.082

= 0.317

The probability that thr household selected is either prosperous or educated is 0.317.

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