CSE 321 Assignment #6
Autumn 1997

Due: Friday, November 21, 1997.

Reading assignment: Finish reading Sections 4.4 and 4.5 of the the text, Discrete Mathematics and Its Applications and then read sections 6.1-6.3.

Practice Problems: page 259, Problem 25; page 280, Problem 13

Problems:

  1. Use the binomial theorem to show that

    C(n,0) + 3 C(n,1) + 9 C(n,2) + ...+ 3k C(n,k) + ... + 3n C(n,n) = 4n.

  2. page 267, Problem 22.

  3. page 267, Problem 32. Justify your answer.

  4. What is the conditional probability that at least 3 heads appear out of 5 flips of a fair coin given that the first flip was tails?

  5. page 280, Problem 16.

  6. page 281, Problem 18. (Show how you derived your answer.)

  7. page 281, Problem 32.

  8. page 364, Problem 4.

  9. (Bonus) The Monty Hall Problem: On the TV show ``Let's make a Deal'' a contestant would be shown 3 doors and allowed to choose one of the 3 doors. Behind these 3 doors would be 2 booby prizes and 1 good prize. Before the chosen door was opened Monty Hall would then open one of the other two doors to display a booby prize and give the contestant a chance to change his/her choice.
    1. Compute the original probability that the chosen door concealed a good prize.
    2. Compute the conditional probability that the 3rd door (not the chosen one nor the opened one) conceals a good prize.
    Based on these calculations what should the contestant do?

  10. (Bonus) Compute the conditional probability that a player has two aces in a Poker hand conditioned on the fact that he has one ace. Compute the conditional probability that a player has two aces in a Poker hand conditioned on the fact that he has the Ace of Hearts.