Question

According to a survey of American households, the probability that the residents own two cars if annual household income is over $75,000 is 73%. Of the households surveyed, 60% had incomes over $75,000 and 72% had two cars.

The probability that the residents of a household own two cars and have an income over $75,000 a year is..... round 3 decimal places

Answer 1

Solution:

Suppose that

Event A :  residents own two cars

Event B : had incomes over  $75,000

Now , from given

P(A) = 72% = 0.72

P(B) = 60% = 0.60

Also given , P(A | B) = 73% = 0.73

But from the definition of the conditional probability ,

P(A | B) = P(A B)/P(B)

0.73 = P(A B)/0.60

P(A B) = 0.73 * 0.60 = 0.438

Answer :

The probability that the residents of a household own two cars and have an income over $75,000 a year is 0.438