STAT 110 – Chapter 4 Basic Probability & Counting Vocabulary

A comprehensive set of vocabulary flashcards covering the fundamental probability and counting concepts addressed throughout the STAT 110 Chapter 4 lecture notes.

Probability

A numerical measure (from 0 to 1) of the likelihood that a specific event will occur.

Classical Probability

A probability obtained by assuming all outcomes in the sample space are equally likely and dividing favourable outcomes by total outcomes.

Empirical Probability

A probability computed from observed frequency data obtained through experiments or past records.

Subjective Probability

A probability value based on personal judgment, intuition, or expert opinion rather than on objective data or equal-likelihood assumptions.

Conditional Probability

The probability of an event A occurring given that another event B has already occurred, written P(A | B).

Sample Space

The set of all possible outcomes of a probability experiment.

Outcome

An individual result of a single trial of a probability experiment.

Event

Any collection of one or more outcomes from the sample space.

Simple Event

An event that consists of exactly one outcome.

Compound Event

An event that contains two or more simple events.

Complement of an Event

All outcomes in the sample space that are not in the event; the probability equals 1 − P(Event).

Equally Likely Outcomes

Situation in which every outcome in the sample space has the same chance of occurring.

Probability Distribution

A table or rule that assigns a probability to every outcome of a random variable such that the probabilities sum to 1.

Probability Experiment

A process that leads to well-defined results called outcomes.

Mutually Exclusive Events

Events that cannot occur at the same time; P(A and B) = 0.

Independent Events

Events where the occurrence of one does not affect the probability of the other; P(A and B) = P(A)·P(B).

Dependent Events

Events where the occurrence of one changes the probability of the other.

Addition Rule (General)

For any events A and B, P(A or B) = P(A) + P(B) − P(A and B).

Addition Rule (Mutually Exclusive)

If A and B are mutually exclusive, P(A or B) = P(A) + P(B).

Multiplication Rule (Independent)

If A and B are independent, P(A and B) = P(A) × P(B).

Multiplication Rule (Conditional)

For any events A and B, P(A and B) = P(A) × P(B | A).

Complement Rule

P(Not A) = 1 − P(A), used to find probabilities of “at least” or “at most” situations.

At Least One Rule

P(at least one success) = 1 − P(no successes).

Tree Diagram

A graphical tool for listing the outcomes of multi-step experiments and calculating their probabilities.

Equally Likely Selection

Choosing items so each individual item has the same probability of selection.

Permutation

An ordered arrangement of objects; the number of permutations of n items taken r at a time is nPr = n! ⁄ (n−r)!.

Combination

An unordered selection of objects; the number of combinations of n items taken r at a time is nCr = n! ⁄ [r!(n−r)!].

Factorial (n!)

The product of all positive integers from 1 to n; used extensively in counting rules.

Fundamental Counting Principle

If one activity can occur in m ways and a second in n ways, the pair can occur in m×n ways.

Probability of the Empty Set

The probability of an impossible event equals 0.

Certain Event

An event that is guaranteed to happen; its probability equals 1.

Equally Likely Events

Two or more events that have the same probability of occurrence.

Relative Frequency

Observed frequency of an event divided by the total number of trials, used to estimate empirical probability.

Complementary Events

Two events whose probabilities add to 1 because together they exhaust the sample space (e.g., rain vs. no rain).

Law of Large Numbers

As the number of trials increases, the empirical probability approaches the theoretical probability.

Replacement

Returning a selected item to the population before the next draw, keeping probabilities unchanged.

Without Replacement

Not returning a selected item, causing the probabilities of subsequent draws to change (dependent events).

Binomial Experiment

A fixed-n sequence of independent Bernoulli trials with constant probability p of success and interest in number of successes.

Probability Range Rule

All probabilities must satisfy 0 ≤ P(E) ≤ 1.

Complement of "Less Than k"

For dice or similar, the complement of getting a number < k is getting a number ≥ k.

At Most k

The event of obtaining k or fewer successes in repeated trials.

At Least k

The event of obtaining k or more successes in repeated trials.

Tree Diagram Branch Probability

The probability of a path equals the product of probabilities along its branches.

Bayes’ Theorem (Concept)

A procedure for finding P(B | A) when P(A | B) and prior probabilities are known.

Complementary Event Pair

An event and its complement together form the entire sample space.

Equally Likely Passwords

When constructing codes where each allowed symbol is chosen with the same likelihood.

Combination of Identical Objects

The number of distinct arrangements of n items with duplicates equals n! divided by factorials of each repetition count.

Simple Random Selection

Each possible subset of a given size has the same probability of being chosen.

Frequency Distribution

A table listing categories or intervals alongside the number of observations in each, basis for empirical probability.

Tree-Level Conditional Probability

Probability at a lower branch conditioned on choices made in earlier branches.