http:^^www.cs.washington.edu^education^courses^321^96f^hw6.html

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Date: Tue, 10 Dec 1996 16:51:45 GMTServer: NCSA/1.4.2Content-type: text/html<HTML><head><title>CSE 321 Assignment #6</title></head><body><h1>CSE 321 Assignment #6<br>Autumn 1996</h1><h3>Due: Friday, November 15, 1996.<br></h3><p>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. <p> Practice Problems: page 259, Problem 25; page 280, Problem 13<p><p> Problems: <ol><p><li> page 258, Problem 16.<p><li> page 259, Problem 26.<p><li> Use the binomial theorem to show that <p> C(n,0) + 2 C(n,1) + 4 C(n,2) + ...+ 2^k C(n,k) + ... + 2^n C(n,n) = 3^n.<p><li> page 267, Problem 22.<p><li> page 267, Problem 32.  Justify your answer.<p><li> What is the conditional probability that at least 3 heads appear outof 5 flips of a fair coin given that the first flip was tails?<p><li> page 280, Problem 16.<p><li> page 281, Problem 18.<p><li> (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 theother two doors to display a booby prize and give the contestant a chanceto change his/her choice.  <ol><li> Compute the original probability that the chosen door concealed a goodprize.<li> Compute the conditional probability that the 3rd door (not the chosenone nor the opened one) conceals a good prize.</ol>Based on these calculations what should the contestant do?<p><li> (Bonus) Compute the conditional probability that a player has two acesin a Poker hand conditioned on the fact that he has one ace.Compute the conditional probability that a player has two aces in a Pokerhand conditioned on the fact that he has the Ace of Hearts.</ol></body></html>

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