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# Expected Value Probabilities

+1
180
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+83

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

#1
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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