Mutually exclusive events

Definition

Two events are mutually exclusive when they have no outcomes in common, so P(A and B) = 0 and P(A or B) = P(A) + P(B).

Worked example

Rolling a 2 and rolling a 5 on a single die throw are mutually exclusive.

A and B are mutually exclusive with P(A) = 0,3 and P(B) = 0,45, so P(A or B) = 0,3 + 0,45 = 0,75.

Where it appears in the exam

Paper 1 probability asks you to identify or prove that events are mutually exclusive, often with a Venn diagram.

Step-by-step method

1. Check whether A and B share any outcomes.
2. If P(A and B) = 0, they are mutually exclusive.
3. Then P(A or B) = P(A) + P(B).
4. Otherwise use P(A or B) = P(A) + P(B) − P(A and B).

Common mistake

Confusing mutually exclusive events with independent events.

Related probability terms

• Independent events
• Fundamental counting principle

Frequently asked questions

What does mutually exclusive events mean in Grade 12 Maths?

Two events are mutually exclusive when they have no outcomes in common, so P(A and B) = 0 and P(A or B) = P(A) + P(B).

Which NSC paper tests mutually exclusive events?

Mutually exclusive events belongs to the Probability section of CAPS Grade 12 Mathematics, which is examined in Paper 1.

How do I practise questions involving mutually exclusive events?

Snap a question that uses mutually exclusive events into the Snap&Learn AI solver, or work through the probability topic guide and NSC past papers.