Call a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Let A be the event that a random household is prosperous and B the event that it is educated. According to the Current Population Survey P (A) = 0.138, P (B) = 0.216, and the probability that a household is both prosperous and educated is:

P (A ⋂ B) = 0.082

Required:

What is the probability P (A ⋃ B) that the household selected is either prosperous or educated?

P (A ⋃ B) = 0.272

Step-by-step explanation:

A = the event that a random household is prosperous and

B = the event that it is educated.

From the survey, we are given:

P (A) = 0.138 P (B) = 0.216 P (A ⋂ B) = 0.082

We want to determine the probability P (A ⋃ B) that the household selected is either prosperous or educated.

In Probability Theory:

P (A ⋃ B) = P (A) + P (B) - P (A ⋂ B)

P (A ⋃ B) = 0.138+0.216-0.082

P (A ⋃ B) = 0.272

The probability P (A ⋃ B) that the household selected is either prosperous or educated is 0.272