Education and income. Call a household prosperous if its income exceeds $100,000

Question

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 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? Find a conditional probability. In the setting of the previous exercise, what is the conditional probability that a household is prosperous, given that it is educated? Explain why your result shows that events A and B are not independent.

Explanation / Answer

4.70

Note that

P(A or B) = P(A) + P(B) - P(A and B) = 0.138 + 0.261 - 0.082 = 0.317 [ANSWER]

*******************

4.71

As

P(A|B) = P(A and B)/P(B) = 0.082/0.261 = 0.314176245 [ANSWER]

As P(A) =/= P(A|B), then A and B are not independent.

*******************

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.