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

Question

Quizplus · Accepted Answer

We can use Bayes' theorem to solve the problem:

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

From the problem statement, we know:

- 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 = 0.69

Therefore, the probability that annual household income is over $50,000 if the residents of a household own two cars is 0.69 or approximately 69%.

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