Year 9 - Maths
Problem solving with theoretical probability
Probability: theoretical probabilities
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit we build upon the concept of likelihood to work more mathematically with more measurable probability using fraction and decimal representations to both interpret and calculate. We revisit and develop ways to represent and compare probabilities.
Lesson Summary
You will learn to use your knowledge of probability to solve problems.
Key Notes
- Knowledge of probability can be applied to real world situations .
- Probabilities can be used to aid decision making.
- Theoretical probabilities come from long-term behaviour and therefore may not be seen in the short-term.
Vocabulary To Learn
- Sample space: A sample space is all the possible outcomes of a trial. A sample space diagram is a systematic way of producing a sample space.
- Tree diagram: Tree diagrams are a representation used to model statistical/probability questions. Branches represent different possible events or outcomes.
- Outcome table: An outcome table is a table that shows all the possible outcomes.
Common Mistakes To Avoid
- When increasing a probability by 50%, pupils may choose to add 50% onto the existing probability rather than multiplying by 1.5.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Knowledge of probability can be applied to real world situations . Probabilities can be used to aid decision making.
2. Use this key word in a maths sentence and explain it clearly. 'Sample space'
A sample space is all the possible outcomes of a trial. A sample space diagram is a systematic way of producing a sample space. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When increasing a probability by 50%, pupils may choose to add 50% onto the existing probability rather than multiplying by 1.5. Correction: Make links to any previous work pupils may have done on increasing by a percentage and emphasise that a percentage increase is being applied to the probability.
More Lessons In This Unit
- Calculating theoretical probabilities from a table (one event) Study Guide
- Calculating theoretical probabilities from lists (one event) Study Guide
- Calculating theoretical probabilities from probability tree diagrams (one event) Study Guide
- Calculating theoretical probabilities from probability trees (two events) Study Guide
- Calculating theoretical probabilities from two-way tables (two events) Study Guide
- Calculating theoretical probabilities from Venn diagrams (one event) Study Guide
- Calculating theoretical probabilities from Venn diagrams (two events) Study Guide
- Checking listing possible outcomes Study Guide
- Comparing multiple representations to calculate theoretical probabilities Study Guide
- Comparing multiple representations to calculate theoretical probabilities for combined events Study Guide
- Summing probabilities Study Guide
- The probability scale Study Guide
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