Answer to a question by Josh:

Ø 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?

Ø 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.

This page has been visited times.

Back to Alex Bäcker's Publications.