Forgetting that probabilities must sum to one is a surprisingly common mistake in IB Maths AI, especially when working with discrete random variables. What makes this error frustrating is that students usually know the rule — they just fail to apply it consistently under pressure.
One reason this happens is fragmented thinking. Students often focus on individual probabilities rather than the distribution as a whole. When questions involve multiple outcomes, students calculate each probability separately and forget to step back and check whether everything adds up logically.
Another cause is overreliance on calculators. When probabilities are generated or manipulated using technology, students trust the numbers without performing basic sense checks. A distribution that sums to more than one or far less than one should immediately raise a red flag, but many students skip this verification step.
Students also struggle when probabilities are given partially. IB frequently provides incomplete distributions and asks students to find missing values. In these cases, the “sum to one” rule becomes the main tool — yet students often try unnecessary algebra instead of using the most direct reasoning.
Expected value questions make this mistake more likely. Students focus on multiplying values and probabilities and forget that the probabilities themselves must form a valid distribution. A small error early on can silently corrupt the entire calculation.
Another issue is misunderstanding what probabilities represent. Some students treat them like independent weights rather than proportions of a whole. This mindset leads to answers that look mathematically neat but are conceptually impossible.
IB examiners rely on this rule as a conceptual checkpoint. Students who explicitly check that probabilities sum to one demonstrate control and understanding. Students who don’t often lose marks even when later working is correct, because the foundation is flawed.
The fix is simple but powerful: always pause and ask whether the probabilities describe a complete system. If all outcomes have been accounted for, the total must be exactly one. This habit alone prevents a large number of avoidable errors.
Once students adopt this global view of probability distributions, discrete random variable questions become far more stable and predictable.
Frequently Asked Questions
Is it a big deal if probabilities don’t sum to one?
Yes. It means the distribution is invalid, even if calculations look correct.
When does IB test this most?
In discrete random variable tables and missing-probability questions.
How can I avoid this mistake in exams?
Always add probabilities at the end as a quick sense check.
RevisionDojo Call to Action
Probability mistakes often come from skipping simple checks. RevisionDojo is the best platform for IB Maths AI because it trains students to validate distributions, spot errors early, and protect marks through good habits. If probability questions feel unstable, RevisionDojo helps you lock them down.
