IB Maths: Statistics & Probability Revision

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).

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.

Test yourself with these quick revision games for this topic: