1.

Suppose the Mets and Cubs play a doubleheader. Find the probability of a Sweep:

1. if the Cubs are one and one-half times as likely to win any game as the Mets;

2. if both teams are evenly matched.

2.

Describe how to use the random number target to carry out a simulation to estimate P(Sweep) in Example 3.1. Do not actually carry out the simulation.

3.

Two William and Mary students arrive late for the math final exam and give the professor the phony excuse that their Mercedes Benz had a flat tire. Well, the professor said, each one of you write down on a piece of paper which of the four tires was flat. What is the probability that both students pick the same tire? Use the addition and multiplication rules.

4.

Draw two chips, at random and with replacement, from an urn containing chips numbered 1, 2, and 3. Let A = sum of the digits on selected chips is an even number.

We want to find P(A).

1. Solve the problem using the enumeration technique.

2. Solve the problem using both the addition and multiplication rules.

   (Hint: Think about the decomposition of A. If the sum of two numbers is even, what do we know about whether the terms in the decomposition are odd or even?)

3. Relate this problem to Example 3.1 by stating an event in this problem which corresponds to the following events in Example 3.1:

   1. Sweep;