Probability of Combined Events — Year 9 Revision Notes
These notes cover sample space diagrams, independent events, and multiplying probabilities for two events — all at Year 9 (Stage 9) level.
Sample space diagrams
A sample space diagram lists all possible outcomes of two events, often as a grid. Rolling two dice gives 36 equally likely outcomes. Once you can see them all, the probability of an event is the number of favourable outcomes divided by the total.
Key Facts & Formulas
- Two dice: 6 × 6 = 36 outcomes
- P = favourable ÷ total
Tips
- Draw the full grid so you do not miss outcomes.
- Count carefully before writing the probability.
Independent events
Two events are independent if one does not affect the other, such as flipping a coin and rolling a dice. For independent events, the probability of both happening is found by multiplying their separate probabilities.
Key Facts & Formulas
- Independent: one does not affect the other
- P(A and B) = P(A) × P(B)
Tips
- Check the events really are independent before multiplying.
- 'And' usually means multiply.
Combining probabilities
To find the probability of two independent events both happening, multiply their probabilities. The probability of rolling a 6 and flipping a head is 1/6 × 1/2 = 1/12. Remember that all the probabilities of an event still add up to 1.
Key Facts & Formulas
- P(A and B) = P(A) × P(B)
- 1/6 × 1/2 = 1/12
Tips
- Multiply for 'and' with independent events.
- Simplify the final fraction.
Revision Checklist
- I can list outcomes in a sample space diagram
- I can find a probability from a sample space
- I can recognise independent events
- I can multiply probabilities for two independent events
Frequently Asked Questions
Do I add or multiply probabilities for two events?
For two independent events both happening ('A and B'), you multiply. Adding is used for 'either/or' situations with a single event. At this stage, 'and' with independent events means multiply.
Build strong foundations in Probability of Combined Events
A free trial class with Teacher Rig helps your Year 9 child master Probability of Combined Events now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Probability of Combined Events develops in IGCSE Probability (Cambridge 0580) →