Year 9 - Maths
Summing 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 show that the probabilities of all possible unique outcomes for a trial, sum to one.
Key Notes
- Summing the probabilities of all possible unique outcomes for a trial gives 1
- Summing the probabilities of non-unique events gives a value not equal to 1
- Knowing that the probabilities of all possible unique outcomes sum to 1 can be used to find unknown probabilities.
- Knowing that probabilities can sum to 1 can be used to find unknown probabilities (different denominators).
Vocabulary To Learn
- Mutually exclusive: Two events are mutually exclusive if they share no common outcome.
Common Mistakes To Avoid
- Pupils may over generalise and think that the sum of all possible events sum to 1. E.g. when rolling a standard six-sided dice, P(multiple of 6) + P(factor of 6) = 1.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Summing the probabilities of all possible unique outcomes for a trial gives 1. Summing the probabilities of non-unique events gives a value not equal to 1.
2. Use this key word in a maths sentence and explain it clearly. 'Mutually exclusive'
Two events are mutually exclusive if they share no common outcome. 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 over generalise and think that the sum of all possible events sum to 1. E.g. when rolling a standard six-sided dice, P(multiple of 6) + P(factor of 6) = 1. Correction: Emphasise that probabilities sum to 1 when the events are mutually exclusive and exhaustive. E.g. in the calculation P(multiple of 6) + P(factor of 6), the outcome '6' is counted twice.
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
- Comparing multiple representations to calculate theoretical probabilities for combined events Study Guide
- Problem solving with theoretical probability Study Guide
- The probability scale Study Guide
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