Year 9 - Maths
Calculating theoretical probabilities from probability trees (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 probability trees (2 events).
Key Notes
- The probability of an outcome can be found with a probability tree diagram showing all possible outcomes for two events.
- The probability of a set of outcomes can be found using a probability tree diagram.
- The probability of a set of outcomes can be found using a probability tree, even when outcomes are not equally likely.
Vocabulary To Learn
- Outcome: An outcome is a result of a trial (e.g. getting heads when flipping a coin once or getting two heads when flipping a coin twice).
- Event: An event is a subset of a sample space. i.e. An outcome or set of outcomes that may occur from a trial (e.g. flipping a coin twice and getting the same result each time).
- 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.
Common Mistakes To Avoid
- When I see a probability tree, I always multiply the probabilities.
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 with a probability tree diagram showing all possible outcomes for two events. The probability of a set of outcomes can be found using a probability tree diagram.
2. Use this key word in a maths sentence and explain it clearly. 'Outcome'
An outcome is a result of a trial (e.g. getting heads when flipping a coin once or getting two heads when flipping a coin twice). Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When I see a probability tree, I always multiply the probabilities. Correction: If a probability tree shows a two-stage trial, then the probability of an outcome is the product of the probabilities of the outcomes at each stage. The probability of an event is the sum of the probabilities of each outcome in the event.
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 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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