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 do not own 2 cars if annual household income is not over $50,000 is:
A)0.12
B)0.18
C)0.45
D)0.70

Question

Quizplus · Accepted Answer

Given that 60% of households have incomes over $50,000 and among these, 80% own 2 cars, it means 48% of all surveyed households (0.60 * 0.80) have incomes over $50,000 and own 2 cars. Since 70% of all households have 2 cars, the remaining 22% (70% - 48%) must have incomes not over $50,000 and own 2 cars. Therefore, 40% of households have incomes not over $50,000 (100% - 60%), and of these, 22% own 2 cars, leaving 18% (40% - 22%) of all households with incomes not over $50,000 that do not own 2 cars. To find the probability that a household with income not over $50,000 does not own 2 cars, divide 18% by 40%, which gives 0.45.

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