Binomial probability distribution (sort of)

[Dave Britten]

(03-03-2016 05:14 PM)lrdheat Wrote:  Geometric distribution allows you to set probability of success on a given trial (assume each trial has that given probability), set number of intended successes, and set probability of having intended # of successes (perhaps you want p=.7 of obtaining your target # of successes).

Geometric distribution sounds fairly close, but everything I'm reading describes it as being based on the first success, rather than a specific, fixed number of successes.

e.g. Suppose I want to know the odds of a particular number of trials being required to roll a die and get 6 twice. A few sample experiments might look like this:

6, 1, 2, 5, 6

1, 3, 3, 4, 3, 5, 4, 4, 6, 4, 4, 3, 5, 2, 4, 6

4, 3, 4, 5, 5, 3, 1, 4, 4, 5, 1, 6, 3, 3, 2, 1, 2, 3, 4, 3, 5, 4, 1, 3, 5, 3, 2, 5, 1, 4, 3, 3, 4, 2, 2, 1, 4, 1, 1, 1, 6

In other words, what are the odds of having to carry out that many trials before hitting the desired number of successes? Is there a more generalized case for the geometric distribution that allows for that?

EDIT: Negative binomial distribution sounds like it might be what I'm after. I'll do some more reading/number crunching.