Year 9 - Maths
Calculating theoretical probabilities from lists (one event)
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 find theoretical probabilities from a list of possible outcomes for one event.
Key Notes
- The probability of an outcome can be found by considering the list of all possible outcomes.
- The probability of a set of outcomes can be found by considering the list of all possible outcomes.
- A list of all possible outcomes can help us find a probability, even when the outcomes are not equally likely.
Vocabulary To Learn
- Theoretical probabilities: 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.
Common Mistakes To Avoid
- Pupils may assume that theoretical probabilities can be also found in cases where individual outcomes are not equally likely (e.g. picking a sweet out of a box where the sweets are different shapes).
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 the list of all possible outcomes. The probability of a set of outcomes can be found by considering the list of all possible outcomes.
2. Use this key word in a maths sentence and explain it clearly. 'Theoretical probabilities'
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 assume that theoretical probabilities can be also found in cases where individual outcomes are not equally likely (e.g. picking a sweet out of a box where the sweets are different shapes). Correction: If the sweets in a box are different shapes then picking a sweet out of the box is not necessarily random. Someone could find their favourite flavour sweet by feeling the different shapes.
More Lessons In This Unit
- Calculating theoretical probabilities from a table (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
- Problem solving with theoretical probability Study Guide
- Summing probabilities Study Guide
- The probability scale Study Guide
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