Question

1. 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. Suppose we know that, P(A) = 0.134, P(B) = 0.254, and the probability that a

household is both prosperous and educated is P(A and B) = 0.080.

This question and the following two all pertain to this scenario.

A. What is Pr(A or B), that is, the probability that a household is either prosperous or

educated?

• A. .034

• B. .388

• C. .120

• D. .308

1a)Are A and B independent?

• A. Yes

• B. No

• C. Can't tell from the information provided.

• D. Neither (a) nor (b).

Answer 1

A:

The probability that a household is either prosperous or educated is

P(A or B) = P(A) + P(B) - P(A and B) = 0.134 + 0.254 - 0.080 = 0.308

Correct option is D.

B:

We have

P(A) * P(B) = 0.134 * 0.254 = 0.034036

Since P(A and B) is not equal to P(A)*P(B) so A and B are not independent.

Answer: B: No