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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.1 The Geometric Series, #38 · Calculus · Series

In a bridge game, what is the average number … of deals…

In a bridge game, what is the average number $μ$ of deals
until you get the best hand? The probability on the first deal
is $p_{1} = \frac{1}{4}$ . Then $p_{2} = (\frac{3}{4}) (\frac{1}{4})$ (probability of missing on the
first time) (probability of winning on the second). Generally $p_{n} = (\frac{3}{4})^{n - 1} (\frac{1}{4})$ . The mean value $μ$ is $p_{1} + 2 p_{2} + 3 p_{3} + \dots =$ ____.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.1 The Geometric Series, #38

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