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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:
- page 258, Problem 16.
- page 259, Problem 26.
- 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.
- page 267, Problem 22.
- page 267, Problem 32. Justify your answer.
- 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?
- page 280, Problem 16.
- page 281, Problem 18.
- (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.
- Compute the original probability that the chosen door concealed a good
prize.
- 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?
- (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.