MYP Maths: Tree Diagrams & Combined Events FAQ

A tree diagram is a branching diagram mapping every possible outcome of two or more events in sequence, with the probability written along each branch. You multiply along a branch to find one specific outcome, and the probabilities branching from any single point must always add up to 1.

Independent events don't affect each other's probability — flipping a coin twice, for example. Dependent events do, like drawing two sweets from a bag without replacing the first, because the second draw's probability changes based on what's already gone. Mixing these up is the fastest way to get the whole tree wrong.

Multiply the probabilities along the branches leading to your outcome, then add the results if more than one branch gives that same outcome. For dependent events, the denominator on the second branch shrinks because one item has already been removed from the group.

"And" means both events happen, so you multiply their probabilities along one branch. "Or" means either event happens, so you add the probabilities of the separate branches that satisfy it. Adding when you should multiply is probably the single most common Criterion A error I see marked wrong.

In MYP 4-5, tree diagrams and combined events are usually assessed under Criterion A (Knowing and understanding) for straight calculations, and Criterion D (Applying mathematics in real-life contexts) when the question sits inside a scenario like weather forecasting or product defects. Some units assess it through Criterion B investigations too.

Expect "calculate" (a numeric answer with working shown), "determine" (find using the given information), "represent" (draw the tree diagram or sample space itself), and "justify" (explain why your method or answer is correct). Each term signals a different depth of response — "justify" needs reasoning, not just a number.

Most marks are lost on three things: forgetting that branch probabilities from one point must sum to 1, using the same denominator for dependent events when it should shrink after each draw, and adding instead of multiplying along an "and" branch. Check these three before submitting any probability answer.

Top-level responses don't just land the right number — they show full working, use correct notation like P(A) rather than just "A," and explain why a method was chosen. In fifteen years of marking this topic, the students hitting level 7-8 always write a sentence of reasoning next to every calculation.

Don't just redo the same worked examples — practise spotting whether events are independent or dependent from the word problem first, since that decision determines your whole diagram. Then time yourself on mixed questions combining "and"/"or" language, because exam papers rarely tell you outright which rule applies.

Not really — MYP Maths cares more about understanding structure than memorising formulas by rote, since you're expected to reason through a tree diagram from scratch. That said, knowing that independent probabilities multiply and mutually exclusive probabilities add saves real time under test conditions.

MYP treats tree diagrams and combined events as a reasoning and application topic, marked against the four MYP criteria with no formal written exam. DP Mathematics AA and AI, under the current syllabus first examined in 2021, extend the same ideas into probability distributions, conditional probability notation, and mark-scheme-based exam questions.

It's not conceptually difficult, but it's a topic where small errors compound — one wrong branch probability throws off every answer that follows it. Most students who struggle aren't bad at maths; they're rushing past the independent-versus-dependent decision right at the start of the question.

The best help isn't reteaching the maths — it's asking your child to explain out loud why an event is independent or dependent before they draw anything, since that's where most errors start. Beyond that, structured practice with full worked solutions matters more than repeated explanation from someone who isn't a maths teacher.