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Tree diagrams for dependent events

Probability · Grade 4–6

Strand: Probability Substrand: Theoretical probability Sparx code: U729 Sparx levels: 2, 3, 4, 5

Key steps (method)

  • Draw the tree with a clear first stage, then the second stage (and more stages if needed).
  • Label each branch with a probability. For each split, the branch probabilities must add to 1.
  • If the events are dependent, update the second-stage probabilities using the new totals (e.g. after taking one out).
  • For an AND question, multiply along the branches of the relevant path.
  • For an OR question, find each relevant path probability then add them.
  • Write the final probability as a simplified fraction/decimal and sanity-check it’s between 0 and 1.

Common mistakes

  • Not making each split add to 1 (missing outcomes or incorrect complements).
  • Mixing up AND (multiply along a path) and OR (add different paths).
  • For dependent events, forgetting to change the second-stage probabilities (e.g. after ‘without replacement’).
  • Dropping or double-counting paths when more than one outcome satisfies the question.
  • Arithmetic errors when multiplying fractions/decimals.

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of Tree diagrams for dependent events (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

Support videos

Notes