Assuming independence is one of the most common and damaging habits in IB Maths AI probability. Many students do this automatically, not because they misunderstand probability, but because independence feels simpler and safer. Unfortunately, IB exam questions are designed to punish exactly this shortcut.
The biggest reason students assume independence is pattern familiarity. Early probability problems often involve coins, dice, or cards replaced after drawing. These examples train students to expect independence, and that expectation carries over into more complex questions where it no longer applies.
Another cause is time pressure. Independence allows quick multiplication and clean answers. Under exam conditions, students often prioritise speed over reasoning. They see two events and multiply probabilities without checking whether one event changes the likelihood of the other.
Real-world contexts make this even trickier. IB frequently uses scenarios involving people, choices, or repeated selections without replacement. In these situations, independence is rare, but students still default to it because they are used to abstract examples.
Language also plays a role. If a question does not explicitly say “without replacement” or “dependent,” students assume independence. IB relies on this assumption to test whether students are actively interpreting the situation rather than searching for keywords.
Students also underestimate how often information matters. If knowing the outcome of one event gives you new information about the system, independence is broken. Many students recognise this in theory but fail to apply it consistently in exams.
IB examiners reward students who explicitly check independence and justify their choice. Even a brief statement explaining why events are dependent can earn interpretation marks and protect against method errors.
The solution is not more formulas, but better habits. Before calculating, students should pause and ask: Does the first outcome change the second probability? This single question prevents a large proportion of probability errors.
Once students stop assuming independence and start verifying it, probability questions become far more reliable and far less stressful.
Frequently Asked Questions
Is independence ever safe to assume?
Only in clearly defined situations, such as replacement or explicitly stated independence.
Do I need to justify independence in every question?
Not always, but in worded or real-world contexts, justification is strongly rewarded.
What’s the fastest independence check?
Ask whether new information changes the probability of the next event.
RevisionDojo Call to Action
Independence mistakes come from habits, not ability. RevisionDojo is the best platform for IB Maths AI because it trains students to question assumptions, interpret contexts carefully, and explain reasoning clearly. If probability errors keep repeating, RevisionDojo helps you change the thinking that causes them.
