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In: Statistics and Probability

In some sports (such as volleyball when I was in high school - scoring rules have...

In some sports (such as volleyball when I was in high school - scoring rules have changed) you can only score a point when it is your serve, and losing when it is your serve does not give up a point but only gives up the serve to your opponent. Suppose your probability of scoring on your serve is p (and of losing the serve is 1 − p) while your opponent’s probability of scoring on their serve is q (so the probability of you regaining the serve is 1 − q).

Find a formula for the probability S that you are the first to score the next point, assuming you currently have the serve. (This takes evaluating an infinite series.) While on the previous part, I have walked you through the process of figuring out what infinite series to evaluate and asked you explicit questions to answer, you should go through the same steps (answering similar questions) and write them out here. As before, get actual numbers for various values of p and q and comment on whether these are what you would expect.

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orchestra answered 2 years ago
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