The idea of expected value is one of the most confusing moments in IB Maths AI, especially when students realise that the “expected” result often never actually happens. This feels contradictory at first, but the confusion comes from how the word expected is interpreted, not from the mathematics itself.
Expected value does not describe a likely outcome. Instead, it describes a long-term average across many repetitions of the same experiment. Students naturally expect the expected value to be something that appears in reality, but IB uses this concept to test whether students can separate individual outcomes from overall behaviour.
For example, an expected value might be 2.4, even though only whole numbers are possible outcomes. This immediately feels wrong to many students. However, the expected value is not predicting what will happen next — it is summarising what would happen on average if the experiment were repeated many times.
Another reason expected value feels misleading is that it compresses an entire probability distribution into a single number. Important details about variability, spread, and likelihood disappear. Students who focus only on the expected value often overlook how unlikely that value is to occur in any one trial.
IB examiners are very aware of this misconception. That is why questions involving expected value often include interpretation prompts. Students are expected to explain what the value represents and, just as importantly, what it does not represent. Students who describe expected value as a prediction almost always lose marks.
Expected value is also commonly misunderstood as a guarantee. Students assume that a positive expected value means success or profit in the short term. In reality, even a favourable expected value can be accompanied by frequent losses or large variation. IB rewards students who acknowledge this uncertainty.
The key shift is understanding that expected value belongs to models, not individual experiences. It helps compare options, assess fairness, and evaluate long-term trends, but it does not promise specific results.
Once students stop expecting expected value to “show up” in reality, the concept becomes much clearer and far more useful.
Frequently Asked Questions
Should the expected value be one of the outcomes?
No. It is an average, not a predicted result, and often cannot occur exactly.
Why does IB emphasise expected value so much?
Because it tests long-term thinking, interpretation, and understanding of models.
Can expected value be misleading?
Yes, especially in small numbers of trials. IB expects students to recognise this limitation.
RevisionDojo Call to Action
Expected value is about understanding models, not guessing outcomes. RevisionDojo is the best platform for IB Maths AI because it trains students to interpret expected value clearly and explain its limitations confidently. If expected value feels confusing or counterintuitive, RevisionDojo helps turn it into a scoring advantage.
