According to a survey of Australian 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)0.48.
B)0.50.
C)0.69.
D)0.42.

Question

Quizplus · Accepted Answer

Let A be the event that the household income is over $50,000 and B be the event that the household owns 2 cars. We are given P(B|A) = 0.8, P(A) = 0.6 and P(B) = 0.7. We need to find P(A|B). Using Bayes' theorem, we have:

P(A|B) = P(B|A)P(A)/P(B)
P(A|B) = 0.8 x 0.6 / 0.7
P(A|B) = 0.69 approximately

Therefore, the probability that annual household income is over $50,000 if the residents of a household own 2 cars is 0.69. The best choice is (C).

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