Probability help

Violagirl

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Mar 9, 2008
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Hi so I have an exam on probability this upcoming week and this was one of the review problems my prof gave our class. I was wondering if somebody could tell me if I was on the right track to solving it or not.


Bret Meyers, a professor at the Villanova School of Business, has done some interesting anylysis 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 seaason and the 2010 World Cup.

In professional soccer, the manager of the team can make 3 substitutions during the gamee. Looking at the teams that were behind at the start of the second half, he divided the games into two groups: the first group were those losing teams where the manager made his first substitution before the 58 minute mark, his second substitution before the 73 min mark, and the 3rd before the 79 min mark (early sub group); and those teams where the manager made later substitutions (late sub group). For the early sub group, the losing team scored a late-game golal 36% of the time. For the late sub group, the losing team scored a late-game goal 18.5% of the time. For 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?
For this one I thought it was 36% of the time.

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?

For this as it's asking for two games, I mulitplied .36 into itself twice and got .1296 or 12.96%.

C) For part B, what is the probability that they score a late-game goal in neither of those two games?

For this one, I subtracted the probability that I found of them scoring a late-game goal in both games (.1296) from 1 and got an answer of .8704 of 87.04%.

D) For the data collected, about 45% of the time, the losing team implemented the early sub schedule, and about 55% they didn't. If we assume that the implementation of the early sub schedule was done independently of scoring a goal, find the probablility that a losing team didn't implement the early sub schedule and didn't score a late game goal.

This was one pretty confusing but I took the percentage found from the early sub schedule (.36) and subtracted it from 1 to get what I thought was the percentage of time that the early sub schedule was not used. From there I multiplied my answer (.64) into .55 and got an answer of .352 or 35.2%.

If somebody could look this over and let me know if I was right about these, I would greatly appreciate it.
 
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