What is a probability?

A probability is a measurement of a possibility (relative to a range of possibilities). Probability theory is a way of formalizing this idea. The most common such formalization–the Kolmogorov axioms–can be thought of as defining: (i) what it means to be a possibility; and (ii) what it means to measure a possibility.

What it means for a quantity to be a probability is a surprisingly contentious topic. It’s an interesting topic–and I encourage you to read about the various possibilities–but for the purposes of this course, we will tend to think of probabilities as a quantification of a degree of belief–e.g. how strongly ones believe that some speaker uttered a high vowel v. a non-high vowel. This interpretation is sometimes referred to as the subjective or Bayesian interpretation. We’ll flesh this idea out as we move through the course.