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eric76
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11 Dec 2013, 10:15 am

As stated, the problem does not guarantee that someone will win. It isn't stated that each of the slips contains a unique number. Therefore, it is possible that more than one slip, perhaps all, may have the same number.



Comp_Geek_573
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13 Dec 2013, 5:23 pm

If each of the 1,000 people was assigned a totally random number, independently of each other, and different people can have the same number, then the probability of NOBODY winning is 0.999^1,000, or about 0.3677. This means the probability of AT LEAST ONE person winning is 1 - 0.3677 = 0.6323.

Now if you KNEW what numbers each person had, then the probability of a given number of people winning will be a multiple of exactly 1/1,000 - since there are only 1,000 "winning number" possibilities, all equally probable! Specifically, the probability of X people winning is n/1,000, where n is the number of lottery numbers shared by X people. For instance, if the numbers 3, 100 and 666 were each shared by four people, then X = 4, n = 3 and so the probability of exactly 4 people winning is 3/1000 in that case.

A raffle is a special case of the above where n = 1,000 for X = 1, and n = 0 for all other X, so it is GUARANTEED that exactly one person will win.


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