Probability
The rules and language of chance, from sample spaces to conditional probability.
23 terms
Addition ruleThe addition rule finds the probability that at least one of two events happens: add the two probabilities, then subtract the overlap.At least one probabilityThe probability of at least one success is 1 minus the probability of no successes, which is far quicker than adding up every separate case.ComplementThe complement of an event is the event that it does not happen, made up of every outcome in the sample space that the original event leaves out.Complement ruleThe complement rule says the probability that an event does not happen is 1 minus the probability that it does.Conditional distributionA conditional distribution is the distribution of one variable within a single row or column of a two-way table, divided by that row or column total.Conditional probabilityConditional probability is the chance one event happens when you count only the cases where a second event holds, so that event is the denominator.Equally likely outcomesOutcomes are equally likely when every outcome in the sample space has the same probability, which is what makes favorable over total valid.EventAn event is any collection of outcomes of a random process, so it is a subset of the sample space and its probability is the chance the result lands in it.General multiplication ruleThe general multiplication rule says P(A and B) equals P(A) times the conditional probability of B given A, and it holds for any two events.Independent eventsTwo events are independent when knowing whether one of them occurred does not change the probability of the other, in either direction.Joint probabilityA joint probability is the chance that two events both happen, written P(A and B), so the same individual or trial has to meet both conditions.Law of large numbersThe law of large numbers says that as independent trials pile up, the average of the results settles toward the true mean and stays near it.Marginal distributionA marginal distribution is the distribution of one variable by itself in a two-way table, built from the row or column totals over the grand total.Marginal probabilityA marginal probability is the probability of one event on its own, read from a row or column total in the margins of a two-way table.Multiplication rule (independent events)The multiplication rule says the probability that two events both happen is the product of their probabilities, but only when the events are independent.Mutually exclusive eventsMutually exclusive events, also called disjoint events, cannot both occur on the same trial, so they share no outcomes and never happen together.OutcomeAn outcome is a single possible result of one trial, and the collection of every outcome for that trial is the sample space.ProbabilityProbability is a number between 0 and 1 that measures how likely an event is: an impossible event has probability 0 and a certain event has probability 1.Sample spaceThe sample space is the set of every possible outcome of a random process, listed so that exactly one of them occurs on each trial.SimulationA simulation imitates a chance process using repeated random outcomes, then estimates a probability from the fraction of trials that give the event.Tree diagramA tree diagram lays out a multi-stage chance process as branches, and the probability of any path is the product of the branches along it.TrialIn probability, a trial is one repetition of a chance process, such as a single coin flip or one draw, and it produces exactly one outcome.Venn diagramA Venn diagram draws events as overlapping circles inside the sample space so unions, intersections, and complements appear as regions.