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Year 10 · Probability Apothecary

Tree
Diagrams

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Probability Apothecary · Tree Drill

Tree Diagrams

A two-stage experiment becomes a tree — branches for each outcome of the first stage, and on each of those, branches for the second. Your job: place the probability on every branch. The tree itself is drawn for you.

Worked Example

A pouch holds 6 stones: 4 obsidian (O), 2 moonstone (M). Draw one, put it back, then draw a second.

With replacement — the second draw has the same probabilities as the first. The two events are independent. Without replacement (you'll see this in Q7 – 8), the second draw depends on the first.

The two rules

Multiply along a path for the probability of one specific outcome:

P(OO) = 4/6 × 4/6 = 16/36 = 4/9

Add across paths for combined outcomes (e.g. "both the same"):

P(both same) = P(OO) + P(MM) = 16/36 + 4/36 = 20/36

For "at least one", take the complement (1 − probability of NONE):

P(at least one O) = 1 − P(MM) = 1 − 4/36 = 32/36

What's coming

Eight questions, graded by how much help you get:

Fractions or decimals both work. Equivalent forms accepted (e.g. 6/10 and 3/5 are both 0.6).

Tree Diagrams  ·  Construct, then apply
Complete

All Eight Sealed

🌳

You've finished all eight construction questions. The mechanics of building a tree from scratch — that's the test-ready skill.

The two rules you've practised:
① Multiply along a path for the probability of a single outcome (e.g. P(BB) = P(B₁) × P(B₂ | B₁))
② Add across paths for combined outcomes (e.g. P(both same) = P(BB) + P(WW))
③ For "at least one", use the complement: 1 − P(none)
④ Without replacement changes the second-stage denominators — total drops by 1, and the colour you took also drops by 1.