Question

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?

Answer 1

P(A ⋃ B)=0.272

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