Visual Reference / Data handling and probability / Probability and tree diagrams

Data handling and probability

Probability and tree diagrams

Explore the probability scale, combined events, tree diagrams, Venn diagrams, and how experimental probability settles toward the theoretical value.

Curriculum rangeYears 6-11

Pick an event and see where it lands on the probability scale.

P(\text{event}) = \dfrac{1}{2} = 0.5 = 50\%

Learning notes

Probability and tree diagrams essentials

Keep these rules beside you while you explore and practise.

1The probability scale

Probability always runs from 0 (impossible) to 1 (certain). It can be written as a fraction, decimal or percentage.

P(\text{event}) = \dfrac{\text{favourable outcomes}}{\text{total equally likely outcomes}}

2Combined events

List every possible outcome in a sample space diagram, then count how many match the event you want.

3Independent vs dependent events

Independent: the first outcome doesn't affect the second (e.g. picking with replacement).

Dependent: the first outcome changes what's left for the second (e.g. picking without replacement).

4Tree diagrams

Multiply along the branches for one combined outcome.
Add up the branches that match the event you want.
All the probabilities from one point should add up to 1.

5Experimental vs theoretical probability

Theoretical probability is calculated; experimental probability (relative frequency) comes from real trials. The more trials you run, the closer relative frequency tends to get to the theoretical probability.

\text{Relative frequency} = \dfrac{\text{times it happened}}{\text{total trials}}

6Venn diagrams

Each circle is an event; the overlap is both happening at once. Everything outside both circles is neither.

P(A \cap B) = \text{both}

P(A \cup B) = \text{either or both}

💡Check yourself: every row of tree branches from the same point must add up to 1, and every Venn diagram region must add up to the total surveyed.