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: 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