First token versus sixth token

Question

A raffle drum holds 8 red tokens and 2 blue tokens, 10 in total. Tokens are drawn out one at a time in order.

What is the probability that the sixth token drawn is blue, and how does it compare to the chance the first token is blue?

Accepted Answer

The surprise here is that the two chances are equal, and symmetry explains why. Every ordering of the 10 tokens is equally likely. So the token in the sixth position is a uniformly random one of the 10, and so is the token in the first position. Neither position is favored. The chance the sixth token is blue: P(	ext{6th is blue})=\frac{2}{10}=\frac{1}{5}=0.2. And the first token is blue with the exact same probability, 	frac{2}{10}=	frac15. Being drawn earlier or later gives no edge. Takeaway. Draw order does not change a position's marginal chance. Any single position, first or sixth or l…

First token versus sixth token

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