Year 9 - Maths
Comparing multiple representations to calculate theoretical probabilities for combined events
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 for combined events.
Key Notes
- The probability of an outcome can be found from multiple representations.
- Each representation can be considered before the most appropriate is chosen.
- Information from one representation can be displayed using a different representation.
Vocabulary To Learn
- 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.
- 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.
Common Mistakes To Avoid
- The probability of an event is the product of the probability of each outcome in the event.
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 found from multiple representations. Each representation can be considered before the most appropriate is chosen.
2. Use this key word in a maths sentence and explain it clearly. '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. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: The probability of an event is the product of the probability of each outcome in the event. Correction: The probability of an event is the sum of the probability of each outcome in the event seen in the sample space of a diagram. For example, in the sample space at the end of a probability tree, or by adding the outcomes in the sample space of a table.
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
- Problem solving with theoretical probability Study Guide
- Summing probabilities Study Guide
- The probability scale Study Guide
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