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This topic covers probability for dependent events where an item is not replaced, so the probabilities change on the second pick — usually shown on a tree diagram. It's examined right across GCSE and iGCSE Maths. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
After the first item is taken, both the number of that item and the total drop by one. Write the second set of branches with the reduced denominator. Then multiply along and add as usual.
Before you start
The prerequisite is tree diagrams and fractions. Keep it sharp for conditional probability.
What you learn
When an item is taken and not put back, the second draw has fewer items — so the second-stage probabilities change. If you take an item and don’t put it back, the next draw has one fewer in total, and one fewer of whatever you took. For ‘at least one’, use 1 − P(none) — usually a single branch to compute. The course works through what changes without replacement, calculating the probabilities and ‘At least one’ via the complement. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Without Replacement is a Probability topic in the GCSE syllabus, covered here at Higher tier. The course is built from 3 concept sections, 2 worked examples and 3 check points before the exam-style set. Nearby topics in the same strand are And / OR rules, Basic Probability, Conditional Probability, Expected Frequency and Mutually Exclusive Events. The Probability revision engine gives you as many extra questions as you want, tracked on your skill tree.
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