Probability_Tutorial

Probability_Tutorial - COMP 170 Tutorial – Intro to...

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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 5-element set model, in which each of the ( 52 5 ) dif- ferent hands of 5 cards is equally likely. (b) The 5-element 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 five-element 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 five-element set model (b) Using the five-element 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 five-element set model (b) Using the five-element 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 five-element set model Problem 1 There are ( 52 5 ) different possible 5-sets. 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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This note was uploaded on 08/25/2010 for the course COMP COMP170 taught by Professor M.j.golin during the Spring '10 term at HKUST.

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Probability_Tutorial - COMP 170 Tutorial – Intro to...

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