Year 9 - Maths
Comparing multiple representations to calculate theoretical probabilities
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 compare and contrast the usefulness of the different representations when calculating theoretical probabilities.
Key Notes
- The probability of an outcome can be calculated from each representation.
- Different representations show the same information in different ways.
- Some representations may be easier to use than others, depending on the context.
Vocabulary To Learn
- Frequency: The frequency is the number of times an event occurs; or the number of individuals (people, animals, etc) with some specific property.
- 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.
- Venn diagram: Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.
- Theoretical probability: Theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.
- Probability tree: Each branch of a probability tree shows a possible outcome from an event or from a stage of a trial, along with the probability of that outcome happening.
Common Mistakes To Avoid
- Venn diagrams are useful when generating a complete list of outcomes and showing the probabilities of that list.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The probability of an outcome can be calculated from each representation. Different representations show the same information in different ways.
2. Use this key word in a maths sentence and explain it clearly. 'Frequency'
The frequency is the number of times an event occurs; or the number of individuals (people, animals, etc) with some specific property. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Venn diagrams are useful when generating a complete list of outcomes and showing the probabilities of that list. Correction: Venn diagrams can be very useful when categorising already known outcomes into events. The Venn diagram can then be used to calculate probabilities. However, Venn diagrams are not as useful when generating a list of outcomes.
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 for combined events Study Guide
- Problem solving with theoretical probability Study Guide
- Summing probabilities Study Guide
- The probability scale Study Guide
Browse all guides in the Year 9 Maths guide library.