Tree diagram probability
A tree diagram helps you organize sequences of outcomes and their probabilities. Each branch shows one possible result, and the probability on a complete path is found by multiplying along the branches.
Method
- Read the branches carefully.
Identify each step in the situation and write the probability for every branch.
- Follow one complete path.
A path represents one specific outcome sequence.
- Multiply the probabilities on that path.
This gives the probability of that exact sequence.
- If the question asks for more than one outcome, add the relevant path probabilities.
Combine only the paths that match the event.
- Simplify the final answer.
Write the probability in lowest terms if possible.
Useful check
Make sure the probabilities leaving the same point add to 1. If they do not, the tree may have been copied incorrectly.
Example of the process
- First event: probability of one branch and probability of the other branch.
- Second event: probabilities from each new branch.
- Final answer: multiply along a path, then add paths when needed.
Tree diagrams are useful because they show every possible outcome clearly and reduce mistakes when events happen in stages.