Chapter 6.6, Problem 5E

In Exercises 1–22, use Bayes’ theorem to calculate the probabilities.

Cars and Income Table 5 gives the distribution of incomes and shows the proportion of two-car families by income level for a certain suburban county. Suppose that a randomly chosen family has two or more cars. What is the probability that its income is at least $75,000 per year?

Table 5
Annual Family Income	Proportion of People	Proportion Having Two or More Cars
$<\$30,000$ $30,000–$44,999 $45,000–$59,999 $60,000–$74,999 $\ge \$75,000$	.10 .20 .35 .30 .05	.20 .50 .60 .75 .90