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 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

Let A be the event that the household has an income over 50,000 and B be the event that the household owns 2 cars. 
We are given:
P(B|A) = 0.80, P(A) = 0.60, and P(B) = 0.70.

Using Bayes' theorem, we can find the probability that the household has an income over 50,000 given that they own 2 cars:

P(A|B) = P(B|A) * P(A) / P(B) 
= 0.80 * 0.60 / 0.70 
= 0.6857

Therefore, the probability that the residents of a household own 2 cars and have an income over $50,000 a year is 0.6857 or approximately 0.48. The closest choice is D.

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