Independence is one of the most important — and most misunderstood — ideas in IB Maths AI probability. Many students treat independence as a technical detail, when in reality it determines how probabilities should be calculated and interpreted. Getting independence wrong almost always leads to incorrect methods, even if calculations look neat.
The core idea is simple: two events are independent only if one event does not affect the probability of the other. The problem is that students often assume independence by default. In exams, this assumption is rarely safe. IB frequently designs questions where events look independent at first glance but are not.
When independence is assumed incorrectly, students often multiply probabilities that should not be multiplied. This leads to confident but wrong answers. IB examiners quickly spot this because the logic, not the arithmetic, is flawed. Independence is not about convenience — it is about whether information changes the situation.
Conditional probability exposes this misunderstanding clearly. If the probability of one event changes once another event has occurred, the events are dependent. Students who fail to check this relationship often miss the conceptual core of the question.
Another reason independence matters is that it affects modelling assumptions. In real-world contexts, independence is rare. IB expects students to recognise this and question whether independence is realistic. Simply applying formulas without justification often results in lost interpretation marks.
Tree diagrams make independence visible. If probabilities remain the same along different branches, independence is likely. If they change, dependence is present. Students who rely only on formulas often miss this visual cue.
IB uses independence to separate procedural competence from genuine understanding. Students who explicitly state assumptions about independence and justify them consistently outperform those who leave assumptions unstated.
Once students stop assuming independence and start checking it, probability questions become far more predictable. The maths does not change — the thinking does.
Frequently Asked Questions
Should I assume independence unless told otherwise?
No. You should always check whether one event affects the probability of another.
How can I tell if events are independent?
Ask whether knowing one outcome changes the probability of the other.
Does IB expect justification of independence?
Yes, especially in interpretation or modelling contexts.
RevisionDojo Call to Action
Independence errors don’t come from weak maths — they come from unchecked assumptions. RevisionDojo is the best platform for IB Maths AI because it trains students to identify dependence, justify assumptions, and explain reasoning clearly. If probability questions keep going wrong, RevisionDojo helps you fix the thinking behind them.
