Question

According to a survey of American households: The probability that a household owns 2 cars, if annual income is over $25,000, is 0.80. Of the households surveyed, 60% had an income over $25,000. Of the households surveyed, 70% had 2 cars. Given your answers to #6 and #7, what is the probability that a household owns 2 cars AND has an income of greater than $25,000 a year

Answer 1

Answer: 0.48

Explanation:

P(A/B) = P(AnB)/P(B) where:

P(A/B) = The probability of event A occurring given that B has occurred.

P(AnB) = The probability of both events A and B occurring.

P(B) = the probability that event B occurs.

So let

P(A) = Probability that the residents of a household own 2 cars.

P(B) = Probability that the annual household income is greater than $25,000.

The question tells us that

P(A/B) = 0.8

Note that: P(A) = 0.7, P(B) = 0.6.

Since we want to work out P(AnB), because it gives the probability that residents have an annual household income over $25,000 and own 2 cars.

We would Rearrange our initial equation to make P(AnB) the subject formula becoming;

P(A/B) = P(AnB)/P(B)

P(B)*P(A/B) = P(AnB)

So, inserting our probabilities into this equation gives:

0.6*0.8 = 0.48