# Chapter 5. Probability

In Chapter 2, I said that a probability is a frequency expressed as a fraction of the sample size. That’s one definition of probability, but it’s not the only one. In fact, the meaning of probability is a topic of some controversy.

We’ll start with the uncontroversial parts and work our way up. There is general agreement that a probability is a real value between 0 and 1 that is intended to be a quantitative measure corresponding to the qualitative notion that some things are more likely than others.

The “things” we assign probabilities to are called events. If E represents an event, then P(E) represents the probability that E will occur. A situation where E might or might not happen is called a trial.

As an example, suppose you have a standard six-sided die and want to know the probability of rolling a six. Each roll is a trial. Each time a six appears is considered a success; other trials are considered failures. These terms are used even in scenarios where “success” is bad and “failure” is good.

If we have a finite sample of n trials and we observe s successes, the probability of success is s/n. If the set of trials is infinite, defining probabilities is a little trickier, but most people are willing to accept probabilistic claims about a hypothetical series of identical trials, like tossing a coin or rolling a die.

We start to run into trouble when we talk about probabilities of unique events. For example, we might like to know the probability that a candidate ...

Get Think Stats now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.