Probability Cheat Sheet

Probability Cheat Sheet

Quick Revision

Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). It is the number of favourable outcomes divided by the total number of outcomes.

1. The Basic Formula

P(event) = Favourable outcomes / Total outcomes

Probability always lies between 0 and 1: 0 ≤ P ≤ 1.

2. The Complement Rule

P(not A) = 1 − P(A)

Often it is easier to find the probability of the event not happening.

3. Addition and Multiplication

P(A or B)  = P(A) + P(B) − P(A and B)
P(A or B)  = P(A) + P(B)           (mutually exclusive events)
P(A and B) = P(A) × P(B)           (independent events)

Mutually exclusive events cannot happen together; independent events do not affect each other.

4. Standard Sample Spaces

A pack of 52 cards: 26 red + 26 black; 4 suits of 13; 12 face cards (J, Q, K × 4); 4 aces.

5. Worked Example

The probability of drawing a king from a pack of 52 cards:

P(king) = 4 / 52 = 1 / 13

The probability of a number greater than 4 on a die:

Favourable = {5, 6} → P = 2 / 6 = 1 / 3

6. Exam Quick Tips

• Probability is always between 0 and 1 — an answer outside that range is wrong.
• Use the complement 1 − P(A) when "at least one" appears.
• For independent events, multiply; for mutually exclusive, add.
• Learn the card facts: 12 face cards, 4 aces, 13 per suit.

Keep revising with the rest of the Maths section:

• All Maths topics
• Statistics Cheat Sheet
• Average Cheat Sheet

How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.