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 Uniform distribution (Posted on 2019-01-25)
6 cards, labeled 1,2, ...6, are randomly put in 3 different envelopes, at least one card in each.

Evaluate the probability of 2,2,2 distribution.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 Easy Peasy (spoiler) | Comment 1 of 9
This is the same as randomly putting in 3 cards where an envelope is allowed to be empty, and evaluating the probability that the distribution is 1,1,1.

Put the first card in a random envelope.  There is a 2/3 probability that the 2nd card goes in an empty envelope, and a 1/3 probability that the 3rd card goes in an empty envelope.

So, the answer is (2/3)*(1/3) = 2/9.

 Posted by Steve Herman on 2019-01-25 09:47:55
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