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Heidi's older sister needs to take either Physics left parenthesis Upper P right parenthesis comma Spanish left parenthesis Upper S right parenthesis comma or Chemistry left parenthesis Upper C right parenthesis this year. She can take the class during any one of six periods left parenthesis 1 through 6 right parenthesis . Is there more than one way to draw a tree diagram to model this​ situation? Explain.

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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) to complete your choice.
A.
Yes. You can make a tree diagram with each subject at the top and the periods as the branches or with the periods at the top and each subject as a branch. The first way provides
  
enter your response here ​outcomes, but the second way provides
  
enter your response here ​outcomes, so the methods provide different outcomes.
B.
Yes. You can make a tree diagram with each subject at the top and the periods as the branches or with the periods at the top and each subject as a branch. Both ways provide the same number of​ outcomes,
  
enter your response here.
C.
No. The tree diagram must be drawn with each subject at the top and the periods as the branches. This provides
  
enter your response here outcomes.
D.
No. A tree diagram cannot be used to model this situation because this is not a compound even

1 answer

To model the situation of Heidi's older sister choosing a subject (Physics, Spanish, or Chemistry) and then selecting a period (1 through 6) using a tree diagram, we indeed have different ways to structure the tree.

Analysis of Options:

  1. Option A suggests that you can structure the tree diagram in two ways (subjects at the top or periods at the top) and that they provide different outcomes. This is somewhat misleading; while you can structure it in two ways, both will ultimately lead to the same number of outcomes, as the relationships between the choices do not change.

  2. Option B correctly states that both ways provide the same number of outcomes. Specifically:

    • If subjects (P, S, C) are on the top level, each subject has 6 branches (for periods), leading to a total of \(3 \times 6 = 18\) outcomes.
    • Conversely, if periods (1 through 6) are on the top level, each period has 3 branches (for subjects), also leading to \(6 \times 3 = 18\) outcomes.

  3. Option C suggests that there is only one correct way to draw the tree diagram, which is not accurate because there are indeed multiple correct ways to draw it, and both yield the same outcome count.

  4. Option D incorrectly states that a tree diagram cannot be used to model the situation at all, which is not the case.

Conclusion:

Given this analysis, the correct choice is B:

B. Yes. You can make a tree diagram with each subject at the top and the periods as the branches or with the periods at the top and each subject as a branch. Both ways provide the same number of​ outcomes, 18.