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There are two boxes, and 10 balloons in each. A guy randomly chooses one box (equal probability) and blows one in that chosen box. He continues this process till he comes over with empty box. What is the probability of leaving exactly 5 balloons in other box?

This is not an exam or competition question that is going live. Source: http://www.zekasorulari.net/balonlar/

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    Exactly 5, or at least 5? – 2017-01-13
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    It asks for exactly. – 2017-01-14

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To leave exactly five, he has to flip a coin $14$ times and get either $9$ heads and $5$ tails or vice versa, then flip the one he already got $9$ of.

To leave at least five he has to flip a coin $15$ times and get at least $10$ heads or at least $10$ tails.

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    Exactly. Thanks, Mr.Millikan. Can you please elaborate it? What is the exact probability of it, in ratios? Thanks. – 2017-01-14