Year 11 - Maths
Experimental vs theoretical probability
Conditional probability
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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, pupils use their knowledge of calculating theoretical probabilities and extend it to calculate conditional probabilities.
Lesson Summary
You will learn to see the impact of sample size and compare theoretical probabilities to experimental ones.
Key Notes
- Different sample sizes can impact the experimental probabilities
- As the sample size increases, the experimental probabilities approach the theoretical probabilities
- A larger sample size is more likely to show a truer estimation of the underlying probability
Vocabulary To Learn
- Trial: A trial is a single, pre-defined test.
- Experiment: An experiment is a repetition of a trial multiple times in order to observe how often each outcome occurs.
- Probability: The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.
Common Mistakes To Avoid
- Pupils may assume that it possible to determine whether a coin (or other object/game) is biased by conducting an experiment with a small number of trials.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Different sample sizes can impact the experimental probabilities. As the sample size increases, the experimental probabilities approach the theoretical probabilities.
2. Use this key word in a maths sentence and explain it clearly. 'Trial'
A trial is a single, pre-defined test. 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 it possible to determine whether a coin (or other object/game) is biased by conducting an experiment with a small number of trials. Correction: The greater the number of trial that an experiment contains, the closer the relative frequency of an outcome gets to its theoretical probability.
More Lessons In This Unit
- Advanced problem solving with conditional probability Study Guide
- Algebra in tree and Venn diagrams Study Guide
- Checking and securing calculating probabilities from diagrams Study Guide
- Checking and securing calculating probabilities from tables Study Guide
- Checking and securing displaying outcomes Study Guide
- Checking and securing exhaustive events Study Guide
- Combinations Study Guide
- Comparing multiple representations to calculate conditional probabilities Study Guide
- Conditional probability in a tree diagram Study Guide
- Conditional probability in a two-way table Study Guide
- Conditional probability in a Venn diagram Study Guide
- Constructing three event Venn diagrams Study Guide
- Experimental probability Study Guide
- Frequency trees Study Guide
- Probabilities in three event Venn diagrams Study Guide
- Probabilities involving algebra Study Guide
- Problem solving with conditional probability Study Guide
- Set notation Study Guide
Browse all guides in the Year 11 Maths guide library.