Statistics and Probability
What the domain tests
Statistics and probability in AI HL tests descriptive statistics, correlation and regression, probability rules, conditional probability, discrete and continuous distributions, and hypothesis testing. The exam emphasises interpretation in context and correct use of GDC distribution and test menus.
Core rules
- Correlation r measures linear association; regression y=a+bx predicts, but correlation is not causation.
- P(A∪B)=P(A)+P(B)-P(A∩B); P(A∩B)=P(A)P(B) only for independent events.
- Conditional probability: P(A|B)=P(A∩B)/P(B).
- Binomial X~B(n,p): P(X=r)=C(n,r)p^r(1-p)^(n-r); mean np; variance np(1-p).
- Normal probabilities use standardization z=(x-μ)/σ or the GDC normal menu.
- Hypothesis test: compare the p-value with the significance level α; reject H0 when p<α.
Worked example
A process has a 60% success rate. In 10 trials, find P(at least 8 successes). X~B(10,0.6), so P(X≥8)=P(X=8)+P(X=9)+P(X=10). P(X=8)=C(10,8)(0.6)^8(0.4)^2≈0.1209; P(X=9)≈0.0403; P(X=10)≈0.0060. The total is about 0.167. “At least 8” includes 8, so the complement would be P(X≤7), not P(X≤8).
Traps
Confusing independent with mutually exclusive; using P(A)P(B) without independence; misreading “at least” and “at most”; concluding causation from r; interpreting a p-value as the probability H0 is true; using the wrong tail in a one-sided test.