Probability — Theoretical and Empirical Concepts

A set of vocabulary flashcards covering core probability concepts from the notes, including theoretical and empirical probability, elementary events, complements, sample spaces, and geometric probability.

Probability (theoretical/classical)

Probability of an event E calculated assuming equally likely outcomes: P(E) = (number of favourable outcomes) / (number of all possible outcomes).

Empirical (experimental) probability

Probability based on observed trials: P(E) = (number of trials in which E occurs) / (total number of trials).

Fair coin

A coin that is unbiased, with heads and tails having equal likelihood on each toss.

Equally likely outcomes

All possible outcomes of an experiment have the same probability.

Elementary event

An event consisting of a single outcome, such as getting heads in a coin toss.

Complement of an event

The event not E (denoted E′ or E^c); P(E) + P(E′) = 1; P(E′) = 1 − P(E).

Sure (certain) event

An event with probability 1; its occurrence is guaranteed.

Impossible event

An event with probability 0; it cannot occur.

Sample space

The set of all possible outcomes of an experiment.

Outcome

A single result from an experiment within the sample space.

Favourable outcomes

The subset of the sample space that makes the event true.

Number of total outcomes

The size of the sample space for an experiment.

Deck of 52 cards

A standard deck with 52 cards, 4 suits of 13 cards each, used to illustrate probabilities (e.g., P(ace) = 4/52).

At least one head

A compound event when tossing two or more coins; at least one of the coins shows heads.

Geometric probability

Probability for continuous outcomes based on ratios of measures (length, area, etc.).

Area-based probability

Geometric probability where P(E) = (favourable area) / (total area) in a region.

Experimental vs theoretical probability

Experimental is based on observed data; theoretical is computed from assumed equal likelihoods; with more trials, they tend to coincide.

Sum of elementary event probabilities equals 1

Axiom: The probabilities of all elementary events in an experiment add up to 1.

P(E) + P(not E) = 1

Complement rule: probability of an event plus the probability of its complement equals 1.