The urn contains B blue balls and R red balls. Each trial consists of drawing one random ball from the urn and observing its color. Then the ball is discarded.
What is the probability that, after N trials, the number of red balls is K?
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Poorly stated question, as it is ambiguous as to whether it is asking for the number of red balls that have been observed or the number that remain in the urn. Oh, "discarded" is spelled with a d. That much I can fix.
Agree with John D'Errico that the Problem Statement is ambiguous. For the record, based on case 5 of the Test Suite, it must be the _observed_ number of red balls that is to be computed.