Probability

Tree Diagrams

Represent multi-stage probability experiments clearly.

Probability overviewVenn diagramsConditional probability

Method

  1. Draw one set of branches for each stage.
  2. Write probabilities on every branch.
  3. Multiply along a path.
  4. Add paths when more than one route gives the desired event.
Anot ABnot BBnot Bmultiply along branches, add separate routes
A tree diagram is a structured way to organise outcomes and probabilities.

Worked example

A bag contains 3 red counters and 2 blue counters. Two counters are taken without replacement. Find the probability of getting two red counters.

\[P(R\text{ then }R)=\frac35\times\frac24=\frac620=\frac310.\]

The second probability changes because the first red counter is not replaced.

Related videos

Tree-diagram practice.

Probability tree diagrams

Watch on this page.

Combined events with tree diagrams

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Independent and combined events

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