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Two old gamblers alternate at rolling a fair 6-sided die until the first 6 comes up....

Two old gamblers alternate at rolling a fair 6-sided die until the first 6 comes up. Compute the probability of the first player winning.

Math   Statistics-And-Probability   
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Answer #1

This is a great question!

The probability of getting a six is 1/6

The first gambler can win either on his first try, third try, fifth try, seventh try,....and so on whenever he gets the 6.

Hence the probability that the first player wins is given by:

P(the first gambler wins) = P(wins on the first try) + P(wins on the third try) + P(wins on the fifth try) + ......

This is the form of infinite geometric progression which can be solved as follows:

Hence the probability of the first gamble winning is 01.5455

If satisfied, please do upvote! Let me know in the comments if anything is unclear. I will reply ASAP

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