Independent events

Definition

Events A and B are independent when P(A and B) = P(A) × P(B). Proving independence in an NSC question means testing this identity with the given probabilities.

Worked example

Two coin tosses are independent: P(two heads) = ½ × ½ = ¼.

P(A) = 0,4, P(B) = 0,5 and P(A and B) = 0,2. Because 0,4 × 0,5 = 0,2, the events A and B are independent.

Where it appears in the exam

Paper 1 probability asks you to prove whether two events are independent by testing whether P(A and B) = P(A) × P(B).

Step-by-step method

1. Find P(A), P(B) and P(A and B) from the question, Venn diagram or table.
2. Calculate P(A) × P(B).
3. Compare it with P(A and B).
4. Conclude: if they are equal, the events are independent.

Common mistake

Concluding that events are independent without showing the calculation.

Related probability terms

• Mutually exclusive events
• Fundamental counting principle

Frequently asked questions

What does independent events mean in Grade 12 Maths?

Events A and B are independent when P(A and B) = P(A) × P(B). Proving independence in an NSC question means testing this identity with the given probabilities.

Which NSC paper tests independent events?

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

How do I practise questions involving independent events?

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