Hypergeometric Distribution and Combinations Suppose there are 30 balls in an urn, 2 red, 2 black and the other 26 white. 
After selecting at random 4 balls without replacing, what is the probability of having at least one red and at least one black ball? Also, what if I were to continue picking balls one by one after the initial 4, how would I go about calculating that. 
I know how to use the hypergeometric distribution to know the probability of getting at least one red ball, but I don't know how to compute for one red and one black. 

I'm afraid I don't know of a clever way to solve this problem, you could enumerate all the possibilities of getting at least one red and one black (e.g. [b,r,white,white] and all permutations, [b,b,r,white] and all perms, [r,r,b,white] and all perms and [r,r,b,b] and all perms), calculate the probabilities for each via the multinomial distribution and then sum them together.
