Many IB Maths AI students are surprised — and sometimes frustrated — when experimental probability does not match theoretical probability. After carefully calculating a probability, they expect real results to line up neatly. When they do not, students often assume a mistake has been made. In reality, this difference is both normal and expected.
Theoretical probability is based on a model. It assumes ideal conditions: fairness, independence, and perfect randomness. When you calculate the probability of rolling a six on a fair die, you are working within this idealised framework. The mathematics is exact, but the situation it describes is simplified.
Experimental probability, on the other hand, is based on observed outcomes. Real experiments are affected by randomness, limited trials, and sometimes imperfect conditions. When the number of trials is small, results can vary widely from theoretical expectations without anything being wrong.
Sample size is the most important factor behind the difference. With only a few trials, random variation dominates. As the number of trials increases, experimental results tend to move closer to theoretical probability. This idea, often linked to long-run behaviour, is central to how IB expects students to reason about probability.
Another reason for disagreement is practical bias. Coins may not be perfectly fair, spinners may not be balanced, and human methods of randomisation are often flawed. IB questions sometimes hint at these limitations, and students are expected to acknowledge them rather than ignore them.
Students also struggle because calculators and formulas make theoretical probabilities feel authoritative. When experiments disagree, students trust the calculation more than the evidence. IB wants the opposite: students should recognise that models describe expectations, not guarantees.
In exams, IB often asks students to compare experimental and theoretical probabilities. The goal is not to decide which one is “right,” but to explain why differences occur. Students who mention randomness, sample size, and assumptions consistently score higher than those who simply state that results are “different.”
Understanding this difference helps students stay calm when numbers do not match. Disagreement does not mean failure — it means the probability model is behaving exactly as it should.
