Year 9 - Maths
Calculating theoretical probabilities from Venn diagrams (two 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 calculate and use theoretical probabilities for combined events using Venn diagrams (2 events).
Key Notes
- The probability of an outcome can be found by considering a Venn diagram showing all possible outcomes for two events.
- The probability of a set of outcomes can be found by using a Venn diagram showing all possible outcomes for two events.
- The probability of a set of outcomes can be found using a Venn diagram, even when the outcomes are not equally likely.
Vocabulary To Learn
- Theoretical probability: A theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.
- Venn diagram: Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.
Common Mistakes To Avoid
- Pupils may struggle with finding the probability of A or B, and may count the outcomes that belong to A and B twice.
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 by considering a Venn diagram showing all possible outcomes for two events. The probability of a set of outcomes can be found by using a Venn diagram showing all possible outcomes for two events.
2. Use this key word in a maths sentence and explain it clearly. 'Theoretical probability'
A theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may struggle with finding the probability of A or B, and may count the outcomes that belong to A and B twice. Correction: If you use an example, such as visiting particular countries, ask the pupils how someone would respond to the question 'have you visited X or Y' if they have in fact visited both countries.
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
- 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
- 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.