**Homework #9 - Probability Topics** --- **85. Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card.** - **G =** card drawn is green - **E =** card drawn is even-numbered **Tasks:** a. List the sample space. b. Calculate $ P(G) $. c. Calculate $ P(G|E) $. d. Calculate $ P(G \text{ AND } E) $. e. Calculate $ P(G \text{ OR } E) $. f. Are $ G $ and $ E $ mutually exclusive? Justify your answer numerically. --- **86. Roll two fair dice separately. Each die has six faces.** a. List the sample space. --- *Page 224* *Chapter 3 | Probability Topics* **Table 3.17** **Problem 94:** In 1994, the U.S. government held a lottery to issue 55,000 Green Cards (permits for non-citizens to work legally in the U.S.). Renate Deutsch, from Germany, was one of approximately 6.5 million people who entered this lottery. Let G = won green card. a. **What was Renate’s chance of winning a Green Card?** Write your answer as a probability statement. b. **In the summer of 1994, Renate received a letter stating she was one of 110,000 finalists chosen. Once the finalists were chosen, assuming that each finalist had an equal chance to win, what was Renate’s chance of winning a Green Card?** Write your answer as a conditional probability statement. Let F = a finalist. c. **Are G and F independent or dependent events?** Justify your answer numerically and also explain why. d. **Are G and F mutually exclusive events?** Justify your answer numerically and explain why. **Problem 95:** Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 64 stamped, addressed envelopes with $10 cash in different classrooms on the George Washington campus. 44% were returned overall. From the economics classes 56% of the envelopes were returned. From the business, psychology, and history classes 31% were returned. Let: R = money returned; E = economics classes; O = other classes a. **Write a probability statement for the overall percent of money returned.** b. **Write a probability statement for the percent of money returned out of the economics classes.** c. **Write a probability statement for the percent of money returned out of the other classes.** d. **Is money being returned independent of the class type?** Answer numerically and explain it. e. **Based upon this study, are economists more selfish than other people? Explain why or why not.** Include numbers to justify your answer. --- The text describes two statistical problems involving probability and conditional probability scenarios. The first problem deals with the probability of winning a green card lottery, considering dependent and independent events, and interpreting conditional probabilities. The second investigates an experiment determining if economists are more selfish based on the return rate of money in an envelope experiment. The problems involve calculating probabilities and interpreting data to draw conclusions.

Homework #9 - Probability Topics --- 85. Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card. - G = card drawn is green - E = card drawn is even-numbered Tasks: a. List the sample space. b. Calculate $ P(G) $. c. Calculate $ P(G|E) $. d. Calculate $ P(G \text{ AND } E) $. e. Calculate $ P(G \text{ OR } E) $. f. Are $ G $ and $ E $ mutually exclusive? Justify your answer numerically. --- 86. Roll two fair dice separately. Each die has six faces. a. List the sample space. --- Page 224 Chapter 3 | Probability Topics Table 3.17 Problem 94: In 1994, the U.S. government held a lottery to issue 55,000 Green Cards (permits for non-citizens to work legally in the U.S.). Renate Deutsch, from Germany, was one of approximately 6.5 million people who entered this lottery. Let G = won green card. a. What was Renate’s chance of winning a Green Card? Write your answer as a probability statement. b. In the summer of 1994, Renate received a letter stating she was one of 110,000 finalists chosen. Once the finalists were chosen, assuming that each finalist had an equal chance to win, what was Renate’s chance of winning a Green Card? Write your answer as a conditional probability statement. Let F = a finalist. c. Are G and F independent or dependent events? Justify your answer numerically and also explain why. d. Are G and F mutually exclusive events? Justify your answer numerically and explain why. Problem 95: Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 64 stamped, addressed envelopes with $10 cash in different classrooms on the George Washington campus. 44% were returned overall. From the economics classes 56% of the envelopes were returned. From the business, psychology, and history classes 31% were returned. Let: R = money returned; E = economics classes; O = other classes a. Write a probability statement for the overall percent of money returned. b. Write a probability statement for the percent of money returned out of the economics classes. c. Write a probability statement for the percent of money returned out of the other classes. d. Is money being returned independent of the class type? Answer numerically and explain it. e. Based upon this study, are economists more selfish than other people? Explain why or why not. Include numbers to justify your answer. --- The text describes two statistical problems involving probability and conditional probability scenarios. The first problem deals with the probability of winning a green card lottery, considering dependent and independent events, and interpreting conditional probabilities. The second investigates an experiment determining if economists are more selfish based on the return rate of money in an envelope experiment. The problems involve calculating probabilities and interpreting data to draw conclusions.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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