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IB Maths Revision

Statistics & Probability

Data analysis, probability, and the binomial and normal distributions.

Learn itInteractive mini-lessons for your exam boardPLAYQuick game on Statistics & ProbabilityVelvet RevisionYour IB Maths course mapFree PDF100 AI prompts for IB Mathematics
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Can a probability be greater than 1?

Statistics & Probability is a core part of IB Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.

Key concepts

Random variableVariable whose value depends on a random event.
Discrete RVTakes countable values like 0, 1, 2,.
Continuous RVTakes any value in an interval, e.g. heights.
ExpectationE(X) = Σ x P(X = x) for discrete X.
VarianceVar(X) = E(X^2) - (E(X))^2.
Standard deviationσ = √Var(X), measures average spread.
Conditional probP(A|B) = P(A∩B)/P(B), given B occurred.
IndependenceP(A|B) = P(A); A unaffected by B.
Multiplication ruleP(A∩B) = P(A|B) × P(B).
Total probabilityP(A) = Σ P(A|B_i) P(B_i) over partition.
Bayes' theoremP(A|B) = P(B|A)P(A) / P(B).
Tree diagramBranching display of conditional probabilities.
Binomial XX ~ B(n, p), counts successes in n trials.
Binomial meanE(X) = np for X ~ B(n, p).
Learn Statistics & Probability step by step

Free interactive mini-lessons: short screens, worked examples and quick checks. Pick your exam board to open its course map, then tap L on this topic:

IB Mathematics: Analysis & Approaches · HLIB Mathematics: Analysis & Approaches · SLIB Mathematics: Applications & Interpretation · HLIB Mathematics: Applications & Interpretation · SL

Common mistakes to avoid

Questions where students often pick the tempting wrong answer — make sure you know the right one:

Can a probability be greater than 1?✗ Yes, some probabilities exceed 1.   ✓ No — probabilities range from 0 to 1.
Is the mean always the best average?✗ Yes, the mean is always best.   ✓ No — outliers can make the median or mode more suitable.

Practise Statistics & Probability — free games

Test yourself with these quick revision games for this topic:

▶ Two Truths, One Lie▶ Reveal Race▶ Connections Grid▶ Falling Words▶ Word Web

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More IB Maths topics

Number & AlgebraFunctionsGeometry & TrigonometryVectorsCalculusDiscrete Mathematics
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100 AI Prompts for IB Mathematics

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