6) The Lakers and the tigers are playing a soccer game. At the end of regulation

Question

6) The Lakers and the tigers are playing a soccer game. At the end of regulation time the score is tied; this forces an overtime. The
rules for the overtime are straightforward. There can be at most three overtime periods. During the first overtime period each team is
given one chance to score. If one team scores and the other does nof score, the game is over and the scoring team is the winner of the
soccer game. If this does not happen, then a second overtime period is played with each team is again given one chance to score. As
before, if one team scores and the other team does not score, the game is over and the scoring team is the winner of the soccer game. IT
this does not happen, then a third overtime period is played with each team is again given one chance to score. As before, if one team
scores and the other team does not score, the game is over and the scoring team is the winner of the soccer game. If this does not
happen, then the game is over and the game is an official tie. The Lakers are a better team than the Tigers. The Lakers score 60% of the
time in an overtime period and the Tigers score 45% of the time in an overtime period. Assume that the event of either team scoring in
an overtime period is independent of the event that the other team scores in that overtime period.
a) Find Pr (the Tigers win the game at the end of the first
overtime period).
b) Find Pr (the lakers win the game).
c) Find Pr (the game is an official tie).

Explanation / Answer

The rules for the overtime are straightforward. The Lakers are a better team than the Tigers. The Lakers score 60% of the time in an overtime period and the tigers score 45% of the time in an overtime period. a) Find Pr (the Tigers win the game at the end of the first overtime period). b) Find Pr (the Lakers win the game). c) Find Pr (the game is an official tie). a: For this to happen, the Tigers must score and the Lakers must not score in period one. What's this probability? b: This requires that the Lakers score in a period where the Tigers do not score. Enumerate the mutually exclusive ways and find the probability of each. This could happen in period one. This could happen in period two: both score in period one OR both don't score in period one This could happen in period three: both score in period one and two OR both don't score in period one and two OR both score in period one but don't score in period two OR both don't score in period one but do score in period two. Are there any other ways? I don't think so. Find the probability of each way and sum them. c: Game ends in a tie... Well, that means no one wins. You can either repeat b: but for the other team winning and then take 1-(answer to b:) - (answer to modified b:) or you can say What's the probability they BOTH... Score/score/score Score/score/don't Score/don't/score Score/don't/don't Don't/score/score Don't/score/don't Don't/don't/score Don't/don't/don't Find the probability of each way and sum it.

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