Combined Probability: Tree Diagrams and Two-Way Tables

List all outcomes of two combined simple events (e.g. tossing a coin and rolling a die) using a two-way table and find basic probabilities from it.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • S4-4
  • S4-3
New NZC (2026)
  • NZC26-P4-PRO-ETP-P-Y9-02
  • NZC26-P4-PRO-ETP-K-Y9-04
  • NZC26-P4-PRO-ETP-K-Y9-05
  • NZC26-P4-PRO-ETP-K-Y9-06

Resources

Terminology

  • Tree diagram
  • Two-way table
  • Combined event
  • Independent events
  • Dependent events
  • With replacement
  • Without replacement
  • Sample space

Task goals

  • Foundation: List all outcomes of two combined simple events (e.g. tossing a coin and rolling a die) using a two-way table and find basic probabilities from it.
  • Proficient: Construct and use a tree diagram for a two-stage event, with and without replacement, to calculate the probability of a specific outcome sequence.
  • Excellence: Use tree diagrams, two-way tables, or Venn diagrams to solve multi-step problems involving independent, dependent, and mutually exclusive events, justifying the reasoning behind each calculation.

Where this fits

What leads into this objective, and where it goes next.

Before

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Combined Probability: Tree Diagrams and Two-Way Tables

Combined Probability: Tree Diagrams and Two-Way Tables

Do

Systematically listing outcomes for the sample space

Statement▸
Year 9 · Probability · Experimental and theoretical probability
NZC26-P4-PRO-ETP-P-Y9-02
Know

Lists, tables, two-way tables, and tree diagrams are useful systematic methods for generating all possible outcomes.

Statement▸
Year 9 · Probability · Experimental and theoretical probability
NZC26-P4-PRO-ETP-K-Y9-04

Next

The official curriculum has no separate Year 10 statements for Probability — Year 9 Probability spans the phase. Try the Statistics strand’s Year 10 statements. Or extend with: Hamiltonian Circuits and Paths in Networks.

Also under S4-4:

Also under S4-3:

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For teachers

Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.