Toss a die until an ace appears. Here the number of trials is a random variable, not a fixed number.

Each of the n trials is either a success or a failure. ``Success'' and ``failure'' are just convenient labels for the two categories of outcomes when we talk about binomial trials in general. These words are more expressive than labels like ``A'' and ``not -- A.'' It is natural from the marksman's viewpoint to call a bull's-eye a success, but in the mice example it is arbitrary which category corresponds to straight hair in a mouse. The word ``binomial'' means ``of two names'' or ``of two terms,'' and both usages apply in our work: the first to the names of the two outcomes of a binomial trial, and the second to the terms p and ** f that represent the probabilities of ``success'' and ``failure.'' Sometimes when there are many outcomes for a single trial, we group these outcomes into two classes, as in the example of the die, where we have arbitrarily constructed the classes ``ace'' and ``not ace.''

We classify mice as ``straight haired'' or ``wavy haired,'' but a hairless mouse appears. We can escape from such a difficulty by ruling out the animal as not constituting a trial, but such a solution is not always satisfactory.

Each die has probability ** f of producing an ace; the marksman has some probability p, perhaps 0.1, of making a bull's-eye. Note that we need not know the value of p, for the experiment to be binomial.