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e. Are "Republican" and "Democrat" complementary events in this data set? Give a reason for your answer. Choose the correct answer below. OA. "Republican" and "Democrat" are not complementary because 1 - P(Republican) = P(Democrat). B. "Republican" and "Democrat" are complementary because 1-P(Republican) = P(Democrat). OC. "Republican" and "Democrat" are complementary because 1 - P(Republican)*P(Democrat). D. "Republican" and "Democrat" are not complementary because 1 - P(Republican) #P(Democrat).

e. Are "Republican" and "Democrat" complementary events in this data set? Give a reason for your answer. Choose the correct answer below. OA. "Republican" and "Democrat" are not complementary because 1 - P(Republican) = P(Democrat). B. "Republican" and "Democrat" are complementary because 1-P(Republican) = P(Democrat). OC. "Republican" and "Democrat" are complementary because 1 - P(Republican)*P(Democrat). D. "Republican" and "Democrat" are not complementary because 1 - P(Republican) #P(Democrat).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The image presents a statistical analysis of a poll regarding voter opinions on the legalization of marijuana, categorized by political affiliation. The table provides details on how different political affiliations (Republican, Democrat, and Independent) responded with either 'Yes' or 'No' to the question of legalization. ### Table Data: - **Republican** - Yes: 147 - No: 124 - Total: 271 - **Democrat** - Yes: 218 - No: 93 - Total: 311 - **Independent** - Yes: 271 - No: 140 - Total: 411 - **Total for all groups** - Yes: 636 - No: 357 - Overall Total: 993 ### Questions and Answers: **a. Probability of being Republican:** - Calculation: (Number of Republicans / Total Sample Size) = \( \frac{271}{993} \times 100 \approx 27.3\% \) **b. Probability of being Democrat:** - Calculation: (Number of Democrats / Total Sample Size) = \( \frac{311}{993} \times 100 \approx 31.3\% \) **c. Probability of being Republican or Democrat:** - Calculation: (Number of Republicans + Number of Democrats) / Total Sample Size = \( \frac{271 + 311}{993} \times 100 \approx 58.6\% \) **d. Mutually Exclusive Events?** - Explanation: Republicans and Democrats are mutually exclusive events because if a voter is identified as "Republican," they cannot simultaneously be a "Democrat." - Correct Answer: A. **e. Complementary Events?** - Explanation: The events are complementary if the probability of one added to the probability of the other equals 1. Here, 1 - P(Republican) ≠ P(Democrat). - Correct Answer: C. This analysis helps understand the distribution of opinions on marijuana legalization among different political affiliations, and the probability concepts involved in determining mutually exclusive and complementary events.
Transcribed Image Text:The image presents a statistical analysis of a poll regarding voter opinions on the legalization of marijuana, categorized by political affiliation. The table provides details on how different political affiliations (Republican, Democrat, and Independent) responded with either 'Yes' or 'No' to the question of legalization. ### Table Data: - **Republican** - Yes: 147 - No: 124 - Total: 271 - **Democrat** - Yes: 218 - No: 93 - Total: 311 - **Independent** - Yes: 271 - No: 140 - Total: 411 - **Total for all groups** - Yes: 636 - No: 357 - Overall Total: 993 ### Questions and Answers: **a. Probability of being Republican:** - Calculation: (Number of Republicans / Total Sample Size) = \( \frac{271}{993} \times 100 \approx 27.3\% \) **b. Probability of being Democrat:** - Calculation: (Number of Democrats / Total Sample Size) = \( \frac{311}{993} \times 100 \approx 31.3\% \) **c. Probability of being Republican or Democrat:** - Calculation: (Number of Republicans + Number of Democrats) / Total Sample Size = \( \frac{271 + 311}{993} \times 100 \approx 58.6\% \) **d. Mutually Exclusive Events?** - Explanation: Republicans and Democrats are mutually exclusive events because if a voter is identified as "Republican," they cannot simultaneously be a "Democrat." - Correct Answer: A. **e. Complementary Events?** - Explanation: The events are complementary if the probability of one added to the probability of the other equals 1. Here, 1 - P(Republican) ≠ P(Democrat). - Correct Answer: C. This analysis helps understand the distribution of opinions on marijuana legalization among different political affiliations, and the probability concepts involved in determining mutually exclusive and complementary events.
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