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Black over White

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A velvet bag contains 9 black marbles and 6 white ones.

You draw them from the bag, one at a time.

When you are finished you have, of course, more black marbles than white.

What is the probability that, in addition, after each draw you have drawn cumulatively more black marbles than white?

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1/5

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1/5

Well done. It might be of interest if you have a concise proof?

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Unfortunately not. I just wrote a recurrent equation (to count possible arrangements of marbles) and solved it using computer.

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