A probability is trivial if it is either one or zero. Suppose we are asking about the probability that Felipe chose a chow chow out of 10 dogs, all of whom are chow chows. The probability is 1, if Felipe did indeed decide to choose a dog, since all of the dogs are chow chows. We would symbolize this trivial probability in the following manner: P(S) = |S| / |S| = 1.

Likewise, suppose we were to ask about the probability of Felipe choosing a golden retriever, if there are 10 dogs and all of them are chow chows. Or suppose we were to ask about the probability of Felipe choosing a chow chow when he decides not to choose any dog. In both cases, the probability is the trivial probability of zero.

We would symbolize this in the following way: P({}) = 0 / |S| = 0. Notice that the P is distributed across the null set, rather than set of actual elements or objects.

Since the sample space of an experiment is a set, it follows that it possesses a power S. The power set of S, which is the sample space of the experiment, refers to all of the events in the experiment. We could refer to this as “pow S.” The maximal set has a probability of 1, the minimal set has a probability of zero (it is the null set) and everything in between has a probability between 0 and 1.

Steinhart, Eric. “More Precisely: The Mathematics You Need To Do Philosophy.” Broadview Press, 2009.