Question

According to a survey of American households, the probability that the residents own a car if annual household income is over $20,000 is 75%. Of the households surveyed, 55% had incomes over $20,000 and 70% had a car. Find the probability that the residents of a household do not own a car and have an income over $20,000.

Answer 1

Solution :

Let us define some events as follows :

A : A resident own a car

B : A resident has income over $20000

Then, A' : A resident do not own a car

We have following informations :

P(A) = 70% = 0.70

P(B) = 55% = 0.55

P(A | B) = 75% = 0.75

We have to find P(A' and B).

P(A' and B) = P(B) - P(A and B)

Let's take P(A | B).

Hence,

P(A' and B) = 0.55 - 0.4125

P(A' and B) = 0.1375

Hence, the probability that the residents of a household do not own a car and have an income over $20,000 is 0.1375.

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