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

#1**+11 **

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