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A local club sells 100 tickets every week from which a winning ticket is randomly selected....

A local club sells 100 tickets every week from which a winning ticket is randomly selected. Assume that every week all 100 tickets are sold and we start afresh the next week with a new lottery. If each ticket costs €3 and you buy 2 tickets every week, how much would you expect to pay overall on tickets by the time you win the lottery for the first time?

Math   Statistics-And-Probability   
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Answer #1

Let be the probability of winning a ticket each week. Then . The probability that he wins a ticket in the the week is . So we see has geometric distribution with parameter . The average number of weeks before the first win is

The amount expected to pay on overall tickets is

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