Independent Events and Tree Diagrams

This lesson covers independent events, the multiplication rule, and the use of tree diagrams — essential topics for the AQA GCSE Mathematics specification. Tree diagrams are one of the most versatile tools for solving probability problems and appear frequently in exam questions at both Foundation and Higher tier.

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Independent Events

Two events are independent if the outcome of one event does not affect the outcome of the other.

Examples

Events	Independent?	Reason
Flipping a coin and rolling a die	Yes	The coin result does not affect the die
Picking a card from a pack, replacing it, then picking again	Yes	Replacement means the pack is the same each time
Picking a card, not replacing it, then picking again	No	The pack has changed — outcomes are affected
The weather today and the result of a die roll	Yes	These are completely unrelated events

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The Multiplication Rule (AND Rule)

For independent events A and B:

P(A and B) = P(A) x P(B)

Worked Example 1