Learning pack · IGCSE handout

Tree Diagrams

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Tree diagrams organise multi-stage probability. Multiply along branches; add across mutually exclusive complete paths.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 28_tree_diagrams_handout.pdf · 28_tree_diagrams_handout_answers.pdf

Full topic summary

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

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.

🎬 Topic videos

Probability Fundamentals (1 of 2: Diagrams, the Product Rule)
Eddie Woo · 6 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Mode & Median of a Continuous Probability Distribution
Eddie Woo · 8 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Fair Dice (Part 1)
Numberphile · 13 min
What makes a die fair? Links sample space, equally likely outcomes, and fairness.
Monty Hall Problem (best explanation)
Numberphile · 4 min
Clearer follow-up explanation of Monty Hall. Use after the short starter version.
Binomial distributions | Probabilities of probabilities, part 1
3Blue1Brown · 13 min
Classroom-ready explain of probability. Use when teaching this topic in Lower Secondary / IGCSE.
Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2
3Blue1Brown · 10 min
Classroom-ready explain of probability. Use when teaching this topic in Lower Secondary / IGCSE.

More Lower Secondary packs

Browse the hub Learning Packs & Summary, or open the compact Tree Diagrams summary.