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?
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, =>
$\frac{N-M}{M} \left(\frac{M}{N}\right)^{1-X}$ => am i correct?