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Two jokers are added to a  52 card deck and the entire stack of  54 cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?

 Jul 26, 2020
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We want to find the expected vaue of j - i, where i and j are the positions of the jokers.

 

We can compute that

 

\(\sum (j - i) = \frac{n^3 - n}{3}\)

 

So the expected value is (n^3 - n)/3/C(n,2).  For n = 54, this is 110/3.

 Jul 27, 2020

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