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 the residents of a household own 2 cars and have an income over $50,000 a year is:
A)0.12
B)0.18
C)0.22
D)0.48

Question

Quizplus · Accepted Answer

We can use the formula for conditional probability:
P(A and B) = P(A|B) * P(B)
where A is the event of owning 2 cars and B is the event of having an income over $50,000.

We are given P(A|B) = 0.8, P(B) = 0.6, and P(A) = 0.7 (from the survey results).
Using the formula for total probability:
P(A) = P(A|B) * P(B) + P(A|B') * P(B')
where B' is the event of having an income at or below $50,000.

Therefore, the probability that the residents of a household own 2 cars and have an income over $50,000 a year is:
P(A and B) = P(A|B) * P(B) = 0.8 * 0.6 = 0.48, option D.

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