According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. What is the probability that the residents of a household own 2 cars and have an income over $25,000 a year?
A) 0.18
B) 0.22
C) 0.48
D) 0.12

Question

Quizplus · Accepted Answer

We know that P(2 cars | income > $25,000) = 0.80 
and P(income > $25,000) = 0.60 
and P(2 cars) = 0.70. 
We want to find P(2 cars and income > $25,000)

Using Bayes' Theorem: 
P(2 cars and income > $25,000) = P(2 cars | income > $25,000) * P(income > $25,000) 
= 0.80 * 0.60 
= 0.48

Therefore, the answer is C.

According to a Survey of American Households, the Probability That