IB Maths Probability Distributions: Binomial, Normal and Beyond (SL and HL)

Probability questions in IB maths look friendly and then quietly take marks away. The maths is often simple; the difficulty is recognising which model applies and writing the answer the way the markscheme expects. This guide focuses on those two skills.

What every course covers

All four courses – AA SL, AA HL, AI SL and AI HL – include:

• Probability basics: Venn diagrams, tree diagrams, conditional probability and independence.
• Discrete random variables and expected value.
• The binomial distribution, X ~ B(n, p), with mean np and variance np(1 − p).
• The normal distribution, standardisation (z-values) and the inverse normal.

What HL adds

• AA HL: Bayes' theorem; continuous random variables defined by a probability density function, with mean, median, mode and variance; and the rules for E(aX + b) and Var(aX + b).
• AI HL: the Poisson distribution, linear combinations of random variables, the central limit theorem, and more statistical testing. In the new course (first exams May 2029) Poisson leaves AI HL, but students sitting exams in 2027 and 2028 still need it.

Which distribution? A quick test

Ask these questions about the situation:

• A fixed number of trials, each a success or a failure, with the same probability, independent? → Binomial.
• A continuous measurement (height, time, mass) that is symmetric around a mean? → Normal.
• (AI HL) Events happening at random at a constant average rate in time or space? → Poisson.
• (AA HL) A probability defined by a function over an interval? → Continuous random variable.

Most lost marks come from skipping this step and pressing calculator buttons straight away.

Setting out working to earn the marks

The markscheme rewards a clear statement of the model. A good answer looks like this:

• *Let X be the number of defective items. X ~ B(20, 0.05).*
• *P(X ≤ 2) = 0.925 (3 s.f.)*

Writing only "binompdf(20, 0.05, 2)" is calculator syntax, not mathematics – and can lose method marks. Always:

1. Define the random variable in words.
2. State the distribution and parameters.
3. Write the probability statement with the correct inequality.
4. Give the answer to three significant figures unless told otherwise.

The traps

• ≤ vs < in discrete distributions. P(X < 3) is P(X ≤ 2) for a binomial.
• "At least one" – use 1 − P(none).
• Inverse normal with the wrong tail. Sketch the curve and shade the area first.
• Standard deviation vs variance in the normal distribution.
• Conditional probability with distributions – for example P(X > 5 | X > 3) – needs the formula, not a single calculator command.

How Maths Bodhi helps with probability

Probability improves fastest with a lot of short, varied questions and honest feedback on presentation:

• A diagnostic to separate understanding gaps from presentation and GDC gaps.
• "Which model?" drills – reading a context and naming the distribution before calculating.
• GDC practice for binomial, normal and (AI HL) Poisson functions, with the written working the markscheme expects.
• Past IB questions grouped by type and marked against the markscheme.

Ajay Vatsyayan (M.Tech, 14+ years teaching maths) teaches IB DP maths at Maths Bodhi and has taught students from schools across Gurgaon, including Pathways World School, The Shri Ram School (Moulsari), Scottish High International School and Lancers International School. Maths Bodhi is independent and not affiliated with any school. Read Ajay's profile, or see our IB probability tutor and IB statistics and probability exam preparation pages.

Home sessions run across Gurgaon – including Golf Course Road and the DLF phases – or online. Book a free demo class.

Related: IB maths AI SL statistics and hypothesis tests, GDC skills for IB maths and the IB DP maths guide for Gurgaon families.

Course content checked against the current IB AA and AI guides and the 2029 update notes by the Maths Bodhi team (October 2026). Teaching approach reviewed by Ajay Vatsyayan.