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The probability of picking two white balls from a lot of black and white balls is $1\over{2}$. If the number of black balls is even, what is the minimum number of black and white balls in the lot?

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    How many trials do you have? Do you have to pick the two white balls on consecutive trials? What have you tried so far?2012-06-11
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    Are you sampling with replacement or without replacement? I think this could affect the answer.2012-06-11
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    @MichaelChernick: If the sampling were with replacement, the probability of picking two white balls would never be $\frac12$, so I assumed it was without replacement.2012-06-11
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    @robjohn Yes that is true since it would have to be 1/sqrt(2) in each case and of course sqrt(2) is not an integer.2012-06-11
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    @MichaelChernick: yes, if $\sqrt{2}$ were rational, it would be an integer. That is, given $p$ white balls and $q$ black balls, the probability of drawing two white balls with replacement would be $\left(\frac{p}{p+q}\right)^2$ which cannot be $\frac12$.2012-06-11

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