You currently have two tests to screen potential stocks to invest in from a list

of 6,000 stocks:

Test

Number of stocks passing the test

A

5,000

B

4,500

a.

[1.5 Points] What is the probability that a stock passes test A? What is the probability

that a stock passes test B?

b.

[3.5 Points] If passing test A and passing test B are independent events, what is the

probability that a stock passes both test A and B? Call this new combined test, test C.

How many stocks do you expect to pass test C?

c.

[5 Points] You've gathered the following information about whether stocks pay

dividends based on whether or not they pass tests A and B:

Given a stock passes test A, the probability it pays a dividend is 0.7

Given a stock passes test B, the probability it pays a dividend is 0.8

Given a stock does NOT pass test A, the probability it pays a dividend is 0.25

Given a stock does NOT pass test B, the probability it pays a dividend is 0.1

What is the (unconditional) probability that a stock pays a dividend?

d.

[4 Points] Suppose you know that probability that a stock passes test C, given it pays a

dividend, is 0.8. What is the probability that a stock pays a dividend, given it passes test

C?

e.

[5 Points] Conducting your tests is costly to you. Test A costs $500 to complete, test B

costs $500, and test C costs $1,000 to complete. If you are interested in figuring which

stocks will pay a dividend, which is the best test for you to use? You should take into

consideration the relative costs of these tests.