I have two dice, one with

*a*faces and the other with

*b*faces. Only one success can come from each die, such that the success rates of the dice are

*1/a*and

*1/b*. I want to know the expected number of times I must throw both dice to such that I obtain an

*n*number of successes.

I know from the means of both the binomial distribution and the negative binomial distribution that I must roll die

*a*an average of

*a*n*times to get

*n*successes and very similar for die

*b*, but I can't seem to figure out how to combine the probabilities to get the answer.