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Odds are ... (Posted on 2017-02-14) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Higher numbers before overflow | Comment 6 of 8 |
(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

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