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the probability that a person who has submitted one entry will win the following? (a) the grand prize (Round your answer to eight decimal places.) If I grand prize is drawn, and 3 first prizes, 30 second prizes, and 450 third prizes are to be awarded, what is

the probability that a person who has submitted one entry will win the following? (a) the grand prize (Round your answer to eight decimal places.) If I grand prize is drawn, and 3 first prizes, 30 second prizes, and 450 third prizes are to be awarded, what is

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Probability in Sweepstakes **Problem Statement:** In a sweepstakes sponsored by Gemini Paper Products, **175,000** entries have been received. If **1** grand prize is drawn, and **3** first prizes, **30** second prizes, and **450** third prizes are to be awarded, what is the probability that a person who has submitted one entry will win the following? **(a)** the grand prize (Round your answer to eight decimal places.) **(b)** a prize (Round your answer to four decimal places.) **Interactive Component:** There is a "Need Help?" section with an option to "Read It." **Answer Submission:** There is a field or button likely for submitting or checking answers based on the provided interface. --- ### Instructions for Students Calculate the probabilities based on the total number of entries and the number of prizes in each category. This problem involves understanding basic probability concepts and precision in answers, as specified (eight and four decimal places). #### Calculation Tips - **Grand Prize Probability (a):** - Formula: \( P(\text{grand prize}) = \frac{\text{number of grand prizes}}{\text{total entries}} \) - For this problem: \( P(\text{grand prize}) = \frac{1}{175,000} \) - **Any Prize Probability (b):** - Formula: \( P(\text{any prize}) = \frac{\text{total number of prizes}}{\text{total entries}} \) - Sum the number of all prizes: \( 1 + 3 + 30 + 450 \) - Determine \( P(\text{any prize}) = \frac{484}{175,000} \) Use these steps to find probabilities and ensure they meet the required decimal precision. Remember to round your answers accurately to the specified decimal places for each part.
Transcribed Image Text:### Probability in Sweepstakes **Problem Statement:** In a sweepstakes sponsored by Gemini Paper Products, **175,000** entries have been received. If **1** grand prize is drawn, and **3** first prizes, **30** second prizes, and **450** third prizes are to be awarded, what is the probability that a person who has submitted one entry will win the following? **(a)** the grand prize (Round your answer to eight decimal places.) **(b)** a prize (Round your answer to four decimal places.) **Interactive Component:** There is a "Need Help?" section with an option to "Read It." **Answer Submission:** There is a field or button likely for submitting or checking answers based on the provided interface. --- ### Instructions for Students Calculate the probabilities based on the total number of entries and the number of prizes in each category. This problem involves understanding basic probability concepts and precision in answers, as specified (eight and four decimal places). #### Calculation Tips - **Grand Prize Probability (a):** - Formula: \( P(\text{grand prize}) = \frac{\text{number of grand prizes}}{\text{total entries}} \) - For this problem: \( P(\text{grand prize}) = \frac{1}{175,000} \) - **Any Prize Probability (b):** - Formula: \( P(\text{any prize}) = \frac{\text{total number of prizes}}{\text{total entries}} \) - Sum the number of all prizes: \( 1 + 3 + 30 + 450 \) - Determine \( P(\text{any prize}) = \frac{484}{175,000} \) Use these steps to find probabilities and ensure they meet the required decimal precision. Remember to round your answers accurately to the specified decimal places for each part.
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