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 adjacent cards that are both black.

I know that this expected outcome, where I would have, for example, case 1 where 20 pairs would happen. Case 1 would have a 1/4 chance of happening, so 20*1/4=5

Then all the cases added together, hence 5+case2+case3+etc would be the answer

confused from here - thanks!

NotydoleM Aug 18, 2023

#1**0 **

There are 52 cards in a deck of cards, of which 26 are black. So, the probability that two cards chosen at random are both black is 26/52⋅25/51 = 25/102.

There are 51 pairs of adjacent cards in a circle of 52 cards. So, the expected number of pairs of adjacent cards that are both black is 51⋅25/102 = 25/2.

Guest Aug 18, 2023