Chapter 6.6, Problem 4E

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

Larceny Rates A metropolitan police department maintains statistics of larcenies reported in the various precincts of the city. It records the proportion of the city population in each precinct and the precinct larceny rate ( $=$ the proportion of the precinct population reporting a larceny within the past year). These statistics are summarized in Table 4. A larceny victim is randomly chosen from the city population. What is the probability that they come from Precinct 3?

Table 4
Precinct	Proportion of Population	Larceny Rate
1 2 3 4	.20 .10 .40 .30	.01 .02 .05 .04