medium Probability
A release-checked medium problem for training Exchangeability.
An urn consists of $2k$, $k \geq 1$, balls of each of $m \geq 2$ colors, of which red and blue are two of them. We select balls one-by-one without replacement from the $2mk$ total balls. Given that in the first $mk$ draws there were exactly $r$ more red balls than blue, find the probability the next ball draw is blue when $k = 12, m = 8,$ and $r = 6$.
This Probability problem is tagged Exchangeability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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