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Unformatted text preview: Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science April 28 Prof. Albert R. Meyer revised April 22, 2010, 668 minutes In-Class Problems Week 12, Wed. Problem 1. [A Baseball Series] The New York Yankees and the Boston Red Sox are playing a two-out-of-three series. (In other words, they play until one team has won two games. Then that team is declared the overall winner and the series ends.) Assume that the Red Sox win each game with probability 3 / 5 , regardless of the outcomes of previous games. Answer the questions below using the four step method. You can use the same tree diagram for all three problems. (a) What is the probability that a total of 3 games are played? (b) What is the probability that the winner of the series loses the first game? (c) What is the probability that the correct team wins the series? Problem 2. To determine which of two people gets a prize, a coin is ﬂipped twice. If the ﬂips are a Head and then a Tail, the first player wins. If the ﬂips are a Tail and then a Head, the second player wins. However, if both coins land the same way, the ﬂips don’t count and whole the process starts over. Assume that on each ﬂip, a Head comes up with probability p , regardless of what happened on other ﬂips. Use the four step method to find a simple formula for the probability that the first player wins. What is the probability that neither player wins?...
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- Spring '11
- Computer Science, Probability theory, Probability space, Prof. Albert R. Meyer