Tree diagrams
Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes
What a learner can do afterwards
- List all 36 outcomes when rolling two dice and find P(total = 7)
- Draw a tree diagram for two successive events and multiply along branches for combined probabilities
- Calculate the probability of a combined event using a sample space diagram and simplify the fraction
The lesson
When one event happens after another, like flipping a coin and then rolling a die, a tree diagram maps out every possible outcome. Draw a branch for each outcome of the first event, then grow more branches out of each one for the second event.
Flip a coin, then roll a die. The coin gives 2 branches: Heads and Tails. From Heads, 6 more branches grow, one for each die face. To find P(Heads and 4), multiply along that path: 1/2 × 1/6 = 1/12.
Multiply along a single path to find its probability. As a check, all the path probabilities from one tree should add up to 1.
A tree diagram maps out every possible outcome step by step, and you multiply along the branches to find the probability of one path.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.