Probability: every key term you need

Probability Basics

Probability = likelihood of event occurring; 0 ≤ P(A) ≤ 1. P(A)=0 impossible, P(A)=1 certain. Frequency approach: P(A) ≈ n(A)/n as n→∞.

Sample Space

Set of all possible outcomes. For coin flip: {H,T}. For die: {1,2,3,4,5,6}. Exhaustive and mutually exclusive.

Complement Rule

P(Ac) = 1 - P(A). Probability of NOT A equals one minus probability of A. Useful for 'at least one' problems.

Addition Rule

P(A∪B) = P(A) + P(B) - P(A∩B). Subtract intersection to avoid double-counting.

Mutually Exclusive Events

A∩B = ∅, so P(A∩B)=0. Then P(A∪B) = P(A) + P(B). Events can't happen simultaneously.

Conditional Probability

P(A|B) = P(A∩B)/P(B); probability of A given B occurred. Requires P(B)≠0.

Independence

Events A and B independent if P(A|B) = P(A); knowledge of B doesn't affect probability of A.

Multiplication Rule

P(A∩B) = P(A)·P(B|A). For independent events: P(A∩B) = P(A)·P(B).

Bayes' Theorem

P(A|B) = P(B|A)·P(A) / P(B). Reverses conditional probability; useful for diagnostic testing.

Counting: Permutations

nPr = n!/(n-r)!; order matters. Arranging r objects from n; same objects in different order = different permutation.

Counting: Combinations

nCr = n!/(r!(n-r)!); order doesn't matter. Choosing r objects from n; same objects = same combination.

Binomial Coefficients

C(n,k) = (n choose k); appears in binomial expansion and probability calculations.

Tree Diagrams

Visual representation of sequential events; branches show outcomes at each stage. Useful for conditional probability.

Two-Way Tables for Probability

Rows and columns represent categorical variables. Use to calculate marginal and conditional probabilities.

Law of Total Probability

P(A) = Σ P(A|Bi)·P(Bi) over all partitions Bi. Condition on all possibilities.

Probability Distributions

List of all possible outcomes and their probabilities; must sum to 1. Can be discrete or continuous.

Unit 3 Summary

Probability rules enable calculating complex probabilities. Conditional probability and independence are key. Counting principles solve combinatorial problems.

More AP Statistics guides

• Designing Studies
• Exploring Bivariate Data
• Random Variables & Distributions
• Sampling Distributions
• Inference for Means