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A <u>tree diagram</u> shows all possible outcomes of two or more events.
Each branch is a possible outcome and can be labelled with a probability.
<u>Step 1</u>: Draw lines (branches) to represent the first set of options (slacks). Write the outcomes on the ends of the branches (brown and black).
<u>Step 2</u>: Draw the next set of branches to represent the second set of options (sweaters). Write the outcomes on the ends of the branches (tan, red and white).
<u>Step 3</u>: Draw the final set of branches to represent the last set of options (shirts). Write the outcomes on the ends of the branches (white and gray).
We assume that the events in this scenario are <u>independent</u> so the probability of the first event happening has no impact on the probability of the second event or the third event happening. Therefore, the probabilities are:
- P(brown slacks) = 1/2
- P(black slacks) = 1/2
- P(tan sweater) = 1/3
- P(red sweater) = 1/3
- P(white sweater) = 1/3
- P(white shirt) = 1/2
- P(gray shirt) = 1/2
Write these on the branches.
