Basic Concepts of Probability

Flashcards covering basic probability concepts, definitions, and rules as presented in the lecture notes.

Probability

Deals with uncertainty and helps us make predictions about the likelihood of various events happening, with values expressed between 0 and 1.

Event

Any collection of results or outcomes of a procedure; anything that happens or can happen.

Outcome

Each possible result of an event.

Simple Event

An outcome or an event that cannot be further broken down into simpler components.

Sample Space

A complete list of all possible simple events for a procedure, consisting of all outcomes that cannot be broken down any further.

P(A)

Denotes the 'probability of event A occurring'.

Probability Value Range

Always a number between 0 and 1. 0 means impossible, 1 means certain.

Relative Frequency Approximation of Probability

Found by observing a procedure and counting the number of times event A occurs, divided by the total number of times the procedure was repeated.

Classical Approach to Probability

Used when a procedure has 'n' different simple events that are equally likely; P(A) is the number of ways A occurs divided by the total number of different simple events.

Subjective Probabilities

P(A) is estimated by using knowledge of the relevant circumstances or personal feelings/experiences, rather than empirical data or equally likely outcomes.

Law of Large Numbers

States that the more times an experiment is repeated, the closer the actual results will get to the expected (theoretical) results.

Complement of an Event

The collection of all the outcomes that are not that event. Its probability is 1 minus the probability of the event.

Rare Event Rule for Inferential Statistics

If, under a certain assumption, an event is extremely unlikely but it happens, then there is reason to doubt the assumption.

Significantly High Result

A result that happens rarely by chance, specifically if the probability of getting 'x or more' successes is 0.05 (5%) or less.

Significantly Low Result

A result that happens rarely by chance, specifically if the probability of getting 'x or fewer' successes is 0.05 (5%) or less.