Question

Call 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 the Current Population Survey, P(A)=0.138, P(B)=0.261, and the probability that a household is both prosperous 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?

Answer 1

Answer: 0.317

Explanation:

Let A be the event that the selected household is prosperous and B the event that it is educated.

Given : P(A)=0.138, P(B)=0.261

P(A and B)=0.082

We know that for any events M and N ,

`\text{P(M or N)=P(M)+P(N)-P(M or N)}`

Thus ,
`\text{P(A or B)=P(A)+P(B)-P(A or B)}`

`\text{P(A or B)}=0.138+0.261-0.082\\\\\Rightarrow\text{ P(A or B)}=0.317`

Hence, the probability P(A or B) that the household selected is either prosperous or educated = 0.317