A urn has (n+1) types of balls, n of unique colors and the rest black. When picking a ball randomly from the urn, a colored (non black) ball has a probability of p of being picked. Each ball of color has equal probability of being picked, ie each has a (p/n) chance of being picked. The urn has infinite balls/we are picking with replacement.
Let X be the number of picks until we get at least 1 of each n colored balls.
What is the Expected value of X ? What is the probability distribution of X ?