🎯 Learning Objectives
- construct two-way outcome tables;
- list combined outcomes without omission;
- find probabilities of sums and conditions;
- distinguish ordered outcomes.
Introduction
This lesson develops Outcome Tables from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Two Fair Dice
| + | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
There are 36 equally likely ordered outcomes.
Worked Example
Sum 7 appears 6 times, so P(sum 7)=6/36=1/6.
(1,6) and (6,1) are different ordered outcomes, although both give sum 7.
Practice Questions
- Find P(sum 2).
- Find P(sum greater than 10).
- Find P(both dice show the same number).
- Why is sum 7 more likely than sum 2?
✅ Check Your Work
Show answers and working
- Only (1,1), so 1/36.
- Sums 11 or 12: (5,6),(6,5),(6,6), so 3/36=1/12.
- Six doubles, so 6/36=1/6.
- Six ordered pairs give 7, but only one pair gives 2.
🧪 Math Lab: Two Dice Outcome Table
Choose a target sum and count the favourable ordered outcomes.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.