EXAMPLE 5 List all outcomes in a sample space using a tree diagram

Suppose our experiment is to toss a fair coin twice.

  1. Construct a tree diagram.
  2. Use the tree diagram to list all the outcomes in the sample space.

Solution

  1. Think of this experiment as a two-stage process:
    • Stage 1: Toss the coin the first time.

    • Stage 2: Toss the coin the second time.

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    Figure 2 shows the tree diagram for the experiment of tossing a fair coin twice. Note the branches for Stage 1: the first time the coin is tossed, it can come up heads or tails. At Stage 2, the tree diagram again has branches for either heads or tails.

  2. The sample space for the experiment of tossing a coin twice is {HH, HT, TH, TT}. There are outcomes in the sample space.
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    Figure 5.2: FIGURE 2 Tree diagram for the experiment of tossing a fair coin twice.

NOW YOU CAN DO

Exercises 31–38.