Unit Overview
Probability
CIE IGCSE MathematicsΒ· 5 min read π 8-10% of combined MCQ and structured paper marks
1. Unit at a Glance
You will start by building foundational knowledge of the 0 to 1 probability scale, calculating probabilities of single equally likely events, and using probability values to predict expected frequencies over repeated trials. You will then progress to more complex scenarios involving combined events and conditional probability, using visual tools like tree diagrams and Venn diagrams to simplify multi-step calculations.
Work through the following sub-topics in order to master all required content for this unit:
Introduction to Probability & Expected Frequency
Learn the probability scale, single event probability calculations, and how to compute expected frequencies for repeated trials.
β β β± 8 min
Combined Events & Conditional Probability
Master calculations for independent and dependent combined events, plus conditional probability using diagrams and given datasets.
β β β β± 10 min
2. Common Pitfalls
Wrong move:
Treating dependent events as independent when calculating combined probability
Why:
This leads to incorrect multiplication of probabilities, as the outcome of the first event changes the probability of the second (e.g. picking items without replacement).
Correct move:
Adjust the second event probability to account for the changed sample space if events are dependent.
Wrong move:
Forgetting the total probability of all mutually exclusive outcomes of an event equals 1
Why:
This causes errors when calculating the probability of an event not happening, or filling in missing values in probability tables.
Correct move:
Use the rule to validate your calculations and find unknown probabilities.
Wrong move:
Using the full sample space for conditional probability calculations
Why:
Conditional probability restricts the sample space to only outcomes where the given condition is true, so using the full sample space gives an inflated, incorrect result.
Correct move:
Restrict the sample space to the given group using the Venn diagram, tree diagram or two-way table β no formula needed.
3. Quick Reference Cheatsheet
Formula/Concept | Description | Use Case | Tier |
|---|---|---|---|
Basic probability of event | Single equally likely events | Core | |
Expected frequency = | Predicted count of over repeated trials | Predicting outcomes for experiments/surveys | Core |
Combined probability for independent events (the / set notation is Extended only) | Events where one outcome does not affect the other | Extended | |
Addition rule for non-mutually exclusive events (the / set notation is Extended only) | Calculating probability of at least one of two events occurring | Extended |
What's Next
Begin your study of this unit with the first sub-topic, Introduction to Probability & Expected Frequency, to build a solid foundational understanding of core probability rules and calculations. Once you have mastered both sub-topics in this unit and completed all included exam-style practice questions, you will be ready to progress to the next unit on Statistics, which builds on probability knowledge to cover data representation and analysis.