Key Concepts

• A sample space or two-way tables can be used to calculate basic probabilities, where you count the number of items of interest and divide by the total number of items.
• If two events are complementary, the sum of their probabilities is 1.
• [latex]P(A \ \mathrm{and} \ B)[/latex] means events [latex]A[/latex] and [latex]B[/latex] must happen in the same outcome.
• [latex]P(A \ \mathrm{or} \ B)[/latex] means either event [latex]A[/latex] or [latex]B[/latex] (or both) must happen in the outcome.
• Conditional probability is calculated as:
  • [latex]P(A|B) = \frac{P(A \ \mathrm{and} \ B)}{P(B)}[/latex]

Glossary

chance experiment: an experiment where the result is not predetermined

complement of an event: the complement of event [latex]A[/latex] consists of all outcomes that are NOT in [latex]A[/latex]

conditional probability: the likelihood that an event will occur given that another event has already occurred. [latex]P(A|B)[/latex] is the conditional probability that event [latex]A[/latex] will occur given that the event [latex]B[/latex] has already occurred.

empirical: a description of an event or experiment that is observed

equally likely: each outcome of an experiment has the same probability

event: a subset of the set of all outcomes of an experiment; the set of all outcomes of an experiment is called a sample space and is usually denoted by [latex]S[/latex]. An event is an arbitrary subset in [latex]S[/latex]. It can contain one outcome, two outcomes, no outcomes (empty subset), the entire sample space, and the like. Standard notations for events are capital letters such as [latex]A, B, C,[/latex] and so on.

experiment: a planned activity carried out under controlled conditions

law of large numbers: as more experiments are done, the experimental probability approaches the theoretical probability

outcome: a particular result of an experiment

probability: a number between zero and one, inclusive, that gives the likelihood that a specific event will occur; also described as long-term relative frequency. Probabilities are between 0 and 1, inclusive.

sample space: the set of all possible outcomes of an experiment