Question
Heidi's older sister needs to take either Physics left parenthesis Upper P right parenthesis or Spanish left parenthesis Upper S 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 event.
Explain.Explain.Explain.Explain.Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
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Question content area bottom
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 event.
Explain.Explain.Explain.Explain.Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
Help me solve this
View an example
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Answers
GPT-4o mini
To determine the correct choice and complete the tree diagram scenario for Heidi's older sister taking either Physics (P) or Spanish (S) at one of six periods (1 to 6), let's break down the options.
1. **Understanding tree diagrams**: A tree diagram can visually represent possible outcomes of a situation by branching out from initial choices. In this case, the initial choices are subjects (Physics or Spanish), and the subsequent choices are the six periods.
2. **Outcomes of tree diagrams**:
- If you place the subjects (P and S) at the top and have branches for each of the six periods from each subject, you would have:
- P → Period 1
- P → Period 2
- P → Period 3
- P → Period 4
- P → Period 5
- P → Period 6
- S → Period 1
- S → Period 2
- S → Period 3
- S → Period 4
- S → Period 5
- S → Period 6
This gives a total of 12 outcomes.
- Conversely, if you place the periods at the top and have branches for each subject from each period, you'd have:
- Period 1 → P
- Period 1 → S
- Period 2 → P
- Period 2 → S
- Period 3 → P
- Period 3 → S
- Period 4 → P
- Period 4 → S
- Period 5 → P
- Period 5 → S
- Period 6 → P
- Period 6 → S
This would also yield the same total of 12 outcomes.
3. **Conclusion**: Both configurations of the tree diagram provide the same total number of outcomes despite the structural differences in the presentation.
Given this analysis, the correct choice is:
**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, 12.**
1. **Understanding tree diagrams**: A tree diagram can visually represent possible outcomes of a situation by branching out from initial choices. In this case, the initial choices are subjects (Physics or Spanish), and the subsequent choices are the six periods.
2. **Outcomes of tree diagrams**:
- If you place the subjects (P and S) at the top and have branches for each of the six periods from each subject, you would have:
- P → Period 1
- P → Period 2
- P → Period 3
- P → Period 4
- P → Period 5
- P → Period 6
- S → Period 1
- S → Period 2
- S → Period 3
- S → Period 4
- S → Period 5
- S → Period 6
This gives a total of 12 outcomes.
- Conversely, if you place the periods at the top and have branches for each subject from each period, you'd have:
- Period 1 → P
- Period 1 → S
- Period 2 → P
- Period 2 → S
- Period 3 → P
- Period 3 → S
- Period 4 → P
- Period 4 → S
- Period 5 → P
- Period 5 → S
- Period 6 → P
- Period 6 → S
This would also yield the same total of 12 outcomes.
3. **Conclusion**: Both configurations of the tree diagram provide the same total number of outcomes despite the structural differences in the presentation.
Given this analysis, the correct choice is:
**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, 12.**