IB Maths Probability & Tree Diagrams: Your Questions Answered

Identify whether events are independent or conditional, then sketch the tree before calculating anything. Label every branch with its probability, multiply along a single branch for AND, and add complete branches for OR. In fifteen years of marking, students who draw the diagram first lose far fewer method marks than those who jump straight to arithmetic.

Independent events don't affect each other, so each branch keeps the same probability value throughout the whole tree — two separate dice rolls, for instance. Conditional probability changes the second branch's value because the first outcome has already happened, most commonly in 'without replacement' problems. Mixing these two up is the single most frequent error I see in AA and AI exam scripts.

Multiply along a single branch of the tree — that's a chain of events happening together, an AND situation. Add across different complete branches — that's alternative routes to the same outcome, an OR situation. If a question asks for 'the probability that…' with two possible paths, you're almost always adding two multiplied terms together.

Without replacement means the sample space shrinks after each draw, so the second level of branches uses a different denominator than the first. Drawing from a bag of 5 red and 3 blue balls, the first branch uses eighths, but the second — given no replacement — uses sevenths. This is the classic conditional-probability trap in both Paper 1 and Paper 2.

Three mistakes recur every year: forgetting to reduce the denominator after 'without replacement', adding branch probabilities that should have been multiplied, and rounding too early so the final answer misses the required three significant figures. Probability appears across both SL and HL content in the current Mathematics: Analysis and Approaches guide, so these errors show up in nearly every session.

Tree diagram questions typically carry 4 to 8 marks in a Paper 1 or Paper 2 structured question, occasionally stretching to 10 marks when combined with expected value or, at HL, Bayes' theorem. Command terms like 'show that' or 'hence find' signal that method marks are available even if your final numeric answer ends up wrong.

You don't have to draw it — mark schemes award method marks for correct multiplication and addition however you set the working out. But for anyone who mixes up conditional probabilities, sketching branches catches the error before it reaches your final answer. I still tell every student I teach to draw it, even under exam pressure.

Probability itself isn't harder in one course — both use identical tree-diagram and conditional-probability skills at SL and HL. The difference is what's built on top: AA HL adds Bayes' theorem and more abstract proof-style questions, while AI HL keeps applications closer to real-world data and calculator-based statistical work.

Maths AA and AI cover the same core probability content — tree diagrams, conditional probability, expected value — at both SL and HL. The real difference is Bayes' theorem, examined only in AA HL, and how each course frames word problems: AI leans on real datasets, AA leans on algebraic structure and notation.

Bayes' theorem is assessed only at HL within Mathematics: Analysis and Approaches — it doesn't appear in AA SL or anywhere in Applications and Interpretation. If you're sitting AA HL, expect at least one exam question linking conditional notation, $P(A|B)$, to a tree diagram with the branches effectively reversed.

Practise past paper questions by topic rather than by year — you'll spot recurring structures like 'without replacement', expected value, and Bayes' theorem far faster than grinding through whole papers. I tell every student to redo any tree diagram question they got wrong within 48 hours, while the mistake's still fresh, not weeks later in a mock.

Focus on conditional probability with and without replacement, expected value from a probability distribution table, and — at HL — Bayes' theorem combined with tree diagrams. These three combinations account for the bulk of probability marks across recent May and November sessions in both Maths AA and AI.

Most students who struggle with probability are skipping the tree diagram and trying to hold the branching logic in their head — that's where conditional probability errors creep in. Encourage your child to draw every branch, even for simple questions; it's a habit examiners reward with method marks even when the final arithmetic slips.

Look for resources that pair worked examples with topic-specific practice questions rather than just answer keys — probability is a skill built through repetition, not memorisation. Topical worksheets that isolate tree diagrams and conditional probability before a full timed paper are usually the most efficient order for revision, especially in the final term before exams.