Shuffling And Deleting

Probability Level 2

We begin with the set {1,2,3,,2016} \{ 1, 2, 3, \ldots , 2016 \} .

We will perform the following operations on the set until the set has only one element left:

  1. Shuffle the set.
  2. Delete the first element.

The probability that the last remaining element is 2016 can be written as AB \dfrac AB, where A A and BB are positive coprime integers. Find A+BA + B.

Note: After shuffling a set of nn distinct elements, any of the n!n! permutations is equally likely to occur.


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