AP Statistics Readers Are Given the Opportunity to Purchase a Polo Shirt Each Year at The

The AP Shirt Problems

AP Statistics Readers are given the opportunity to purchase a polo shirt each year at the reading session. Each year that the AP Statistics program has been in existence there has been a shirt offered that has a unique color. Two AP Statistics Readers, Brenda and Rich, have been attending the readings for almost all of the years that the test has been given. Brenda and Rich both purchased AP Statistics shirts for the following years, shown here with the respective colors.

Year Color

2000 red

2001 black

2002 green

2003 tan

2004 yellow

For problems 1 through 5, assume that Brenda and Rich have decided to wear AP Statistics shirts each day of their one week summer institute and not wear the same shirt twice. They have also decided to independently select the shirt they will wear randomly from the shirts in the table above.

1. What is the probability that both Brenda and Rich will wear a red shirt on the first day of the institute?

2. What is the probability that Brenda and Rich will wear the same color shirt on the first day of the institute?

3. If Brenda and Rich both wear red shirts on the first day of the institute, what is the probability that they will both wear green shirts on the second day of the institute?

4. If Brenda and Rich wear the same color shirt on the first day of the institute, what is the probability that they will wear the same color shirt on the second day of the institute?

5. If Brenda and Rich do not wear the same color shirt on the first day of the institute, what is the probability that they will wear the same color shirt on the second day of the institute?

For problems 6 and 7, assume that the same conditions apply except Rich really has two AP Statistics shirts that Brenda does not have (Blue and Aqua) and decides to actually choose from all seven shirts.

6. What is the probability that both Brenda and Rich will both wear a red shirt on the first day of the institute?

7. What is the probability that Brenda and Rich will wear the same color shirt on the first day of the institute?