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A. Monty Hall plays a game with his TV show participants to teach a valuable lesson in probability. There are three curtains denoted A, B, and C on stage with a prize behind each. One of the prizes is quite valuable, the other two have only nominal value. In the first step the participant, named Marlon Vos Savant, picks a curtain, although at this point it remains closed. In the second step Monty then opens one of the two remaining curtains to reveal a prize of nominal value. In the third step the participant, Marlon, chooses between the two remaining closed curtains; i.e., stick with his original choice or switch.

1. In the first step, what is the probability that Marlon picks the curtain behind which there is the valuable prize?

2. In the first step, what is the probability that Marlon has not picked the door with the prize behind it?

3. In the second step, what is the probability that Monty pulls aside a curtain with a nominal prize behind it?

4. In the third step, there are two closed curtains.  One of the two closed curtains is the one that Monty didn't pick to open.  From Marlon's perspective, what is the probability that the prize is behind the curtain that Monty didn't pick?

5. In the third step should Mary switch her choice or stick with her original choice?

B. Rosebud Press publishes a magazine titled Sledding.  The following information about weekly newsstand demand at a price of $3 per copy has been determined:

6. What is the expected number of weekly magazine sales?

7. What is the variance of weekly magazine sales?

8. When price is $3, what is expected revenue?

Marilyn Brando has a newsstand at which she sells Sledding.  Each week she must decide how many magazines to stock. Each week she buys the magazines from the publisher for $1 per copy. She sells the magazines for $3 per copy. At the end of the week she returns any unsold copies and receives $0.50 per copy.

9. Suppose that M. Brando stocks 5 copies of the magazine and sells three, what profit does she earn?

10. Suppose that M. Brando stocks 5 copies of the magazine and sells four, what profit does she earn?

11. Suppose that Brando stocks 5 copies of the magazine, what will be her expected weekly profit?

12. Suppose that Brando stocks 4 copies of the magazine and sells two, what will be her profit?

13. Suppose that Brando stocks 4 copies of the magazine, what will be her expected weekly profit?

14. How many copies of Sledding should Brando stock in order to maximize her expected weekly profit from sales of the magazine?