# Probability Urn Question

An urn contains n balls, all different colors. A person draws a ball randomly, records the color before replacing it. The person must record all colors in order to receive a large prize. If m colors have been recorded so far, what is the probability that it will take exactly x draws to get a new color?

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## 1 Answer

Hint: Think of each draw as a Bernoulli trial, with "success" meaning you get a colour that's not one of the $m$ you've already seen.

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Okay using your hint. By Bernoulli trial, the probability of a success would be : ((N-M)/M). Probability of a failure is M/N. now the probability that it will take x trials to get a success would be, => ((N-M)/M) * (M/N)^(1-X). is this the right direction? – user19974 Nov 23 '11 at 7:24
((N-M)/M)) * ((M/N)^(1-X)) => did not use proper brackets last time. am i correct? – user19974 Nov 23 '11 at 7:27