Answer to a question by Josh:

 

      If I have N pancakes in a pan, how many times must
I flip a randomly drawn pancake before I achieve a
50% chance of having flipped all N pancakes at least
once?

      p(0) = p(flipped=N given N flips) = (N-1)/N x (N-2)/N
x ... x 1/N

p(flipped=N given N+1 flips) = p(flipped=N given N
flips) x (1+(1- N x
p(flipped=N given N flips)))

eg. p(1) = p(flipped=N given N+1 flips) = p0 +
(1-p0) x N x p0

For any given N you can then calculate what's the
first i such that p(i) >=.50. The number of trials is i+2
(1 because I called the first p zero rather than 1, 1 because the first
trial is not covered in the above formulation) where p(i) is the iteration used.
Thus p(0) gives n of trials needed =2.

Let's say N=2. What is the answer?
p(0) = p(flipped=N given N flips) = (2-1)/2 = .5
thus the answer to your problem with N=2 is 2 trials.

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