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A standard deck of cards contains 52 cards. These 52 cards are arranged in a circle, at random. Find the expected number of pairs of adjacents cards that are both Aces or Kings

 Oct 30, 2023
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There are 52 cards in a deck, so there are 51 pairs of adjacent cards. Each pair has an equal probability of being Aces or Kings, which is 524​⋅513​=22112​. So, the expected number of pairs of adjacent cards that are both Aces or Kings is:

Expected number = 51 * (\frac{12}{221}) = \boxed{\frac{40}{221}}

 Oct 30, 2023

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