Ch5_6examples

Ch5_6examples - Problem 1 Bret Myers a professor at the...

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Problem 1 Bret Myers, a professor at the Villanova School of business, has done some interesting analysis of substitutions in professional soccer games. He analyzed every single game played in the top English, Spanish, Italian and German professional leagues in 2009-2010, as well as all the games played during the 2010 Major League Soccer season and the 2010 World Cup. In professional soccer, the manager of the team can make 3 substitutions during the game. Looking at the teams that were behind at the start of the second half, he divided the games into two groups: the Frst group were those losing teams where the manager made his Frst substitution before the 58 minute mark, his second substitution before the 73 minute mark, and 3 rd before the 79 minute mark (early sub group); and those teams where the manager made later substitutions (late sub group). ±or the early sub group, the losing team scored a late-game goal 36% of the time. ±or the late sub group, the losing team scored a late-game goal 18.5% of the time. ±or teams that were tied or teams that were winning, it didn't matter when the substitutions were made. A) What is the probability of the losing team scoring a goal given that the manager followed the early sub schedule? This is the conditional probability: P(goal | early substitution) = 0.36 from the description above. B) Assume each game is independent. A team decides to implement the early sub strategy in the next two games that they are losing. What is the probability that they score a late-game goal in both of those games? Here, you need to apply the multiplication rule: P( goal in 1 st game | early sub AND goal in 2 nd game | early sub) = P(goal | early sub) * P(goal | early sub) because independent. = 0.36 * 0.36 = 0.1296 C) ±or part B, what is the probability that they score a late-game goal in neither of those two games? The answer is very similar to part B, except you are working with the complement:

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This note was uploaded on 02/28/2012 for the course ECON 111 taught by Professor Aaa during the Summer '11 term at UIBE.

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Ch5_6examples - Problem 1 Bret Myers a professor at the...

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