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jmc

counting and probability senior

Problem

Two jokers are added to a card deck and the entire stack of cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?
Solution
Each card has an equal likelihood of being either on top of the jokers, in between them, or below the jokers. Thus, on average, of them will land between the two jokers. Multiplying this by the 52 yields our answer of .
Final answer
\frac{52}{3}