A **probability** is a number between 0 and 1 that expresses the chance of an event. Probabilities must satisfy some specific rules like: i) if two things can’t happen simultaneously then the probability that one or the other happens is the sum of their probabilities, and ii) the probability of something equals one minus the probability of the opposite thing.

The **relative frequency interpretation** of probability defines probabilities as the relative frequency or proportion of time that something happens if you repeat the process over and over again independently forever.

Two events are **mutually exclusive** if they can’t both happen at the same time.

Two events are **independent** if knowing that one event has occurred doesn’t change the chances for the other event.

A **subset** is a part of a larger group of values. For example, the list {1,4, 7} is a *subset* of the larger *set* {1,3,4,6,7,10}.

When a chance process results in a number, the **expected value** is the long run average value when the basic process is repeated over and over again.

A **simulation** is used to study a chance process by applying a computer model to mimic what might happen in the real world. By repeating the simulation many times we can develop a detailed picture of the behavior of the chance process under study in different circumstances.

A **random number** is a value produced in a computer simulation following the set of values and probabilities needed to study a model of a chance process.

The **Law of Large Numbers** says that averages or proportions in a random sample are likely to be more stable (get closer to their expected population values) when there are more trials while sums or counts are likely to be more variable. This does not happen by compensation for a bad run of luck since independent trials have no memory.