Topic 3: Chapter 3 — Probability

Probability of an event

P(event) = Number of favourable outcomes / Total number of outcomes.

Sample space

List of all possible outcomes.

Outcome

A possible result of an experiment.

Event

List of favourable outcomes.

Equally likely outcomes

Outcomes with the same chance of occurring.

Probability scale

From 0 (impossible) to 1 (certain).

Venn diagrams

Visualise union (∪), intersection (∩), and complement (').

Addition rule

P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Mutually exclusive

P(A ∩ B) = 0; then P(A ∪ B) = P(A) + P(B).

Product rule for independent events

P(A ∩ B) = P(A) × P(B).

Conditional probability

P(A|B) = P(A) if independent.

Multi-stage experiments

Use arrays and tree diagrams.

Dependent events

Outcome of one affects the other.

Probability of an event

P(E) = number of favourable outcomes / total outcomes

Probability scale

0 (impossible) to 1 (certain)

Complementary events

P(E') = 1 - P(E)

Equally likely outcomes

Each outcome has same chance of occurring

Venn diagrams

Used to represent sets and probability visually

Two-way tables

Organise outcomes from two variables/events

Tree diagrams

Show all possible outcomes in stages

Mutually exclusive events

Cannot occur at the same time (P(A ∩ B) = 0)

Independent events

P(A ∩ B) = P(A) × P(B)

Conditional probability

P(A | B) = P(A ∩ B) / P(B)

Relative frequency

Experimental probability = number of successes / total trials

Expected value

E(X) = Σ[x × P(x)]

Simulation

Use of models or random methods to estimate probabilities