1. Suppose a company fleet of 20 cars contains 7 cars that do not meet government exhaust emissions standards and are therefore releasing excessive pollution. Moreover, suppose that a traffic policeman randomly inspects 5 cars. What is the probability that he will find 2 cars that exceed pollution control standards?

2. From a group of 7 democrats and 12 republicans, a committee of 4 is selected at random. What is the probability that the committee consists of 2 democrats and 2 republicans.

3. Suppose that in a set of 20 accounts 6 contain errors. If an auditor samples 4 to inspect, what is the probability that:

(a) No errors are found? (b) 4 errors are found? (c) No more than 2 errors are found? (d) At least 3 errors are found?

4. A football team has 22 players for offense and 25 players for defense and kicking. If four team captains are chosen randomly, what is the probability that three of the captains will be from the offense?

Answers1. 0.3874

2. 0.357

 3. (a) No errors are found? 0.2066

(b) 4 errors are found? 0.0031(c) No more than 2 errors are found? 0.939(d) At least 3 errors are found? 0.0611

4. ANS: 0.2158