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Week05Notes - Stat 311 Introduction to Mathematical...

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Stat 311 Introduction to Mathematical Statistics Zhengjun Zhang Department of Statistics, University of Wisconsin, Madison, WI 53706, USA September 29-October 1, 2009 Extra Examples for Chapter 3 Example 3.6 Charles claims that he can distinguish between beer and ale 75 percent of the time. Ruth bets that he cannot and, in fact, just guesses . To settle this, a bet is made: Charles is to be given ten small glasses, each having been filled with beer or ale, chosen by tossing a fair coin. He wins the bet if he gets seven or more correct. Find the probability that Charles wins if he has the ability that he claims. Find the probability that Ruth wins if Charles is guessing. Example 3.12 A poker hand is a set of 5 cards randomly chosen from a deck of 52 cards. Find the probability of a 1. royal flush (ten, jack, queen, king, ace in a single suit). 2. straight flush (five in a sequence in a single suit, but not a royal flush). 3. four of a kind (four cards of the same face value). 4. full house (one pair and one triple, each of the same face value). 5. flush (five cards in a single suit but not a straight or royal flush).
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