You face an urn with 5555 cards in it, each has a non-zero integer written on it. Nothing is said about the distribution of those numbers. You are told to draw randomly a card, copy the number, return it back, shuffle and draw randomly a card, then write down the sum of both numbers, say S.

(i) Prove: The probability of S being an even number is higher than S being odd.
(ii) Is it true for any initial number of cards? Comment.

(In reply to Higher numbers before overflow by Charlie)

Based on Charlie's numerical evidence I conjecture that the probability is (N+1)/2N.

Posted by xdog on 2017-02-14 16:24:49