According to a survey of American households,the probability that the residents own 2 cars if annual household income is over $50,000 is 80%.Of the households surveyed,60% had incomes over $50,000 and 70% had 2 cars.The probability that annual household income is over $50,000 if the residents of a household own 2 cars is:
A)0.42
B)0.48
C)0.50
D)0.69

Question

Quizplus · Accepted Answer

Using Bayes' theorem, we want to find P(income > $50k | 2 cars).

P(income > $50k | 2 cars) = P(2 cars | income > $50k) * P(income > $50k) / P(2 cars)

From the problem, we are given:
- P(2 cars | income > $50k) = 0.8
- P(income > $50k) = 0.6
- P(2 cars) = 0.7

Plugging these values into Bayes' theorem, we get:
P(income > $50k | 2 cars) = 0.8 * 0.6 / 0.7
P(income > $50k | 2 cars) = 0.69

Therefore, the answer is D, 0.69.

According to a Survey of American Households,the Probability That the Residents