# Problem 1 The 1987 World Series was tied at two games a...

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Math 230.01, Fall 2012: HW 2 Solutions This homework is due at the beginning of class on Thursday January 26th, 2011 . You are free to talk with each other and get help. However, you should write up your own solutions and understand everything that you write. Problem 1. The 1987 World Series was tied at two games a piece before the St. Louis Cardinals won the fifth game. According to the Associated Press, “The numbers of history support the Car- dinals and the momentum they carry. Whenever the series has been tied 2-2 the team that won the fifth game won the series 71% of the time.” If momentum is not a factor and each team has a 50% chance of winning each game (independently of the previous games), what is the probability that the Game 5 winner will win the series? (The World Series is a best of 7 series of games played between the two teams. That is, the first team to win a total of 4 games wins the series.)
Problem 2. Suppose Alice and Bob play the following game. Alice flips three coins while Bob flips two. Alice wins if she has more Heads showing than Bob. a) Find the probability that Alice wins.
b) What is Alice’s probability of winning if she flips n + 1 coins and Bob flips n coins? Is this surprising? 1