Date: Tue, 10 Dec 1996 16:51:45 GMT Server: NCSA/1.4.2 Content-type: text/html CSE 321 Assignment #6

CSE 321 Assignment #6
Autumn 1996

Due: Friday, November 15, 1996.

Reading Assignment: Read sections 4.4, 4.5, and 6.1 of the text. The following problems are from the Third Edition of the text.

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

Problems:

  1. page 258, Problem 16.

  2. page 259, Problem 26.

  3. Use the binomial theorem to show that

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

  4. page 267, Problem 22.

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

  6. 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?

  7. page 280, Problem 16.

  8. page 281, Problem 18.

  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.