Historically, the first method of assigning probabilities to the outcomes of a random event is due to Bernoulli. His recipe is this: when there is no reason to do otherwise, assign all outcomes equal probability. This is called the principle of insufficient reason, or principle of indifference. We will discuss an extension of the principle of insufficient reason, called the principle of maximum entropy. It applies in cases where one does not expect the outcomes to fall out uniformly.

We will describe the principle of maximum entropy and see how it works in some examples. In particular, we will see how this principle provides a unifying conceptual role for several standard probability distributions.