Topic summary · IGCSE handout

Tree Diagrams summary

Tree diagrams organise multi-stage probability. Multiply along branches; add across mutually exclusive complete paths.

Open Learning Sheet — Tree Diagrams Download Tree Diagrams answers PDF

Files: 28_tree_diagrams_handout.pdf · 28_tree_diagrams_handout_answers.pdf · free public downloads · diagrams in the PDFs

Key learning points

With replacement vs without: probabilities on later branches may change.
All branch probabilities from a node sum to 1.
Label fractions clearly — cancelling too early can hide mistakes.

Worked example 1 — Two-stage AND

Fair coin twice. $P(HH)$ ?

Working

\tfrac{1}{4}

Multiply along branches.

Worked example 2 — OR of paths

P(exactly one head in two flips)?

Working

\tfrac{1}{2}

Add exclusive paths.

Worked example 3 — Without replacement

Bag: 3 red, 2 blue. P(two reds)?

Working

\tfrac{3}{5}\times\tfrac{2}{4}=\tfrac{3}{10}

Update the total after first draw.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.

Open Learning Sheet Answers PDF

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