Grade 11

Probability

Quantify chance — from basic rules and Venn diagrams to counting principles and conditional probability.

Basic Probability Rules

Probability is a number between 0 and 1 that measures how likely an event is. 0 means impossible; 1 means certain.

Theorem

P(A) = \frac{\text{number of favourable outcomes}}{\text{total number of equally likely outcomes}}

Theorem

P(A^\prime) = 1 - P(A)

The complement $A'$ means "A does not happen". Together $A$ and $A'$ cover every possibility.

Theorem

P(A \cup B) = P(A) + P(B) - P(A \cap B)

You subtract $P(A \cap B)$ because when you add P(A) and P(B) you counted the overlap twice.

For mutually exclusive events (can't happen at the same time): $P(A \cup B) = P(A) + P(B)$

Worked Example

A bag has 4 red, 3 blue and 5 green balls. One ball is drawn at random. Find: (a) P(red), (b) P(not blue), (c) P(red or green).