A binomial random variable models the number of successes in

trials, where the trials are independent and the only options on each trial are success and failure. A generalization of this called a multinomial distribution can be obtained by allowing more than two possibilities on each trial. When there are three possibilities on each trial, call them "perfect", "acceptable", and "failing", the result is a trinomial random variable. Letting

be the number of perfects and

the number of acceptables in

trials, the image is a rendering of the joint probability mass function of

and

. The cuboid whose lower-left corner is at

has height equal to the probability of

perfects and

acceptables in

trials. Note that if

is the probability of a trial being perfect and

the probability of a trial being acceptable, then the probability of failure on the trial is

.