This deep dive covers Systematic Listing Methods within Sample Spaces for GCSE Mathematics. Revise Sample Spaces in Probability for GCSE Mathematics with 11 exam-style questions and 20 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 4 of 6 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 4 of 6
Practice
11 questions
Recall
20 flashcards
Systematic Listing Methods
Method 1: Tree Diagrams
Tree diagrams help visualize all possible outcomes systematically.
Example: Two Coin Flips
First Coin Second Coin Outcome
H ——————— H ——————— HH
| ——————— T ——————— HT
|
T ——————— H ——————— TH
——————— T ——————— TT
Method 2: Tables/Grids
Useful when dealing with two separate experiments.
Example: Rolling Two Dice
| Die 1 \ Die 2 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | (1,1) | (1,2) | (1,3) | (1,4) | (1,5) | (1,6) |
| 2 | (2,1) | (2,2) | (2,3) | (2,4) | (2,5) | (2,6) |
| ... | ... | ... | ... | ... | ... | ... |
Total outcomes: 6 × 6 = 36
Method 3: Multiplication Principle
If one event has m outcomes and another has n outcomes, together they have m × n outcomes.
Examples:
- Two coins: 2 × 2 = 4 outcomes
- Three coins: 2 × 2 × 2 = 8 outcomes
- Die and coin: 6 × 2 = 12 outcomes
- Two dice: 6 × 6 = 36 outcomes