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How Do You Use a Tree Diagram to Count the Number of Outcomes in a Sample Space?

Jenny is getting ready for a night on the town and is trying to decide what to wear. She has 3 shirts: one blue, one purple, and one red. She also could wear jeans or a skirt, and she could wear sandals or high heels. How many different outfits could Jenny make?

Summary

  1. Let's label each shirt, bottom, and type of shoe with an easy to remember letter
  2. We can figure out how many outcomes there are by making a tree diagram
  3. First list each shirt she could wear
  4. For each shirt, we can list each choice she has for bottoms
  5. Then, for each bottom, we can list each choice she has for shoes
  6. Each branch of the tree represents a different outcome, so count them to see how many outfits she could wear
  7. She has 12 outfits to choose from!

Notes

    1. We need to organize the kinds of shirts, bottoms, and shoes she can wear
    1. She has two options: jeans (J) or a skirt (S)
    2. We can pair each choice of shirt with each bottom
    1. She has two options: sandals (S) or high heels (H)
    2. We can pair each choice of bottom with each pair of shoes
    1. Each branch of the tree represents a different outcome, so count them to see how many outfits she could wear