question archive You are about to play a best 3 out 5 games of black jack against your brother (the series stops as soon as one player wins 3 games)

You are about to play a best 3 out 5 games of black jack against your brother (the series stops as soon as one player wins 3 games)

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You are about to play a best 3 out 5 games of black jack against your brother (the series stops as soon as one player wins 3 games). Assume you each have a 50% chance of winning each game and the games are independent of one another. What is the probability there will be "sweep" in the series meaning either one of you wins the contest in just 3 games without a 4th or 5th game being necessary?

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