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?
Probability question on picking balls
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probability
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0How 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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1Are you sampling with replacement or without replacement? I think this could affect the answer. – 2012-06-11
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0@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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0@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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0@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