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Unformatted text preview: COMP 170 Tutorial – Intro to Probability Last updated: May 2, 2010 Problem 1 What is the probability that a hand of 5 cards chosen from an ordinary deck of 52 cards, will consist of cards of the same suit? Problem 1 What is the probability that a hand of 5 cards chosen from an ordinary deck of 52 cards, will consist of cards of the same suit? The first question is Problem 1 What is the probability that a hand of 5 cards chosen from an ordinary deck of 52 cards, will consist of cards of the same suit? The first question is What is the sample space (and associated probability weights)? Problem 1 What is the probability that a hand of 5 cards chosen from an ordinary deck of 52 cards, will consist of cards of the same suit? The first question is What is the sample space (and associated probability weights)? There are actually two different logical answers: (a)The 5element set model, in which each of the ( 52 5 ) dif ferent hands of 5 cards is equally likely. (b) The 5element permutation model , in which each of the 52 5 different ordered hands of 5 cards is equally likely. Problem 1 What is the probability that a hand of 5 cards chosen from an ordinary deck of 52 cards, will consist of cards of the same suit? Problem 1 (a) Using the fiveelement set model What is the probability that a hand of 5 cards chosen from an ordinary deck of 52 cards, will consist of cards of the same suit? That is, assume that each of the ( 52 5 ) different hands of 5 cards is equally likely Problem 1 (a) Using the fiveelement set model (b) Using the fiveelement permutation model What is the probability that a hand of 5 cards chosen from an ordinary deck of 52 cards, will consist of cards of the same suit? That is, assume that each of the ( 52 5 ) different hands of 5 cards is equally likely That is, assume that each of the 52 5 different ordered hands of 5 cards is equally likely Problem 1 (a) Using the fiveelement set model (b) Using the fiveelement permutation model What is the probability that a hand of 5 cards chosen from an ordinary deck of 52 cards, will consist of cards of the same suit? That is, assume that each of the ( 52 5 ) different hands of 5 cards is equally likely That is, assume that each of the 52 5 different ordered hands of 5 cards is equally likely Both models will give the same answer! Problem 1 What is the probability that a hand of 5 cards chosen from an ordinary deck of 52 cards, will consist of cards of the same suit? (a) Using the fiveelement set model Problem 1 There are ( 52 5 ) different possible 5sets. Among these possibilities, there are 4(13 · 12 · 11 · 10 · 9) / 5! ways of choosing one suit. Thus, the probability is (52 · 12 · 11 · 10 · 9) / 5!...
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 Spring '10
 M.J.Golin
 Computer Science, Probability theory, Playing card, Suit, Playing cards

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