MathDB

Problem 4

Part of 1999 French Mathematical Olympiad

Problems(1)

eating candies in a specific way

Source: 1999 France MO P4

4/10/2021
On a table are given 19991999 red candies and 66616661 yellow candies. The candies are indistinguishable due to the same packing. A gourmet applies the following procedure as long as it is possible:
(i) He picks any of the remaining candies, notes its color, eats it and goes to (ii). (ii) He picks any of the remaining candies, and notes its color: if it is the same as the color of the last eaten candy, eats it and goes to (ii); otherwise returns it upon repacking and goes to (i).
Prove that all the candies will be eaten and find the probability that the last eaten candy will be red.
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