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The cards of a standard 52-card deck are dealt out in a circle. What is the expected number of pairs of adjacent cards which are both black? Express your answer as a common fraction.

MATHEXPERTISE  Oct 24, 2018
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For each pair of cards, the probability that they are both black is \(\frac{26}{52} * \frac{25}{51} = \frac{25}{102}\), so since there are 52 pairs in the circle, the expected number of pairs which are both black is \(\frac{25}{102} * 52 = \frac{650}{51}\).

 

Our answer should be \(\boxed{\frac{650}{51}}\).

KnockOut  Oct 24, 2018

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