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Simpler probability problem? (Posted on 2015-08-11) Difficulty: 1 of 5
An urn contains 5 black and 20 white marbles. They are to be drawn one at a time until all of one color has been exhausted.

What is the probability that the color of the first draw correctly predicts the first color exhausted?

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re(4): solution | Comment 9 of 14 |
(In reply to re(3): solution by Ady TZIDON)

The color of the first one to be exhausted does not change even if the drawing were to continue until all 25 have been drawn. Making the assumption that all 25 would be drawn simplifies the calculation in that we only need to see what would have been chosen as the last marble of the 25, considering all permutations of the remaining 24 marbles equally likely. Whatever color that is, the opposite color was the first to be exhausted as that one was the last to be exhausted if continued to the last marble.

That is what I calculated and the correct answer is 1/3, not 2/3.

  Posted by Charlie on 2015-08-12 12:08:07
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