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1. A poll conducted by Pugh Research found 75% of Americans want the next president to be middle-aged (35-65 years old). 57% responded that they preferred a president willing to compromise on issues to accomplish action rather than make decisions strictly along partisan ideals. 48% of the respondents fell into both categories. (a) What is the probability a randomly selected American wants the next president to be middle-aged or willing to compromise? (b) What is the probability a randomly selected American wants the next president to be middle-aged or willing to compromise but not both? Interpret the result. (c) In a random group of four Americans, what is the probability none of them fell into at least one of the categories? (d) In a random group of six Americans, what is the probability at at most five want the next president to be middle-aged? (e) In a random group of five Americans, what is the probability at least one wants a president that is willing to compromise?

1. A poll conducted by Pugh Research found 75% of Americans want the next president to be middle-aged (35-65 years old). 57% responded that they preferred a president willing to compromise on issues to accomplish action rather than make decisions strictly along partisan ideals. 48% of the respondents fell into both categories. (a) What is the probability a randomly selected American wants the next president to be middle-aged or willing to compromise? (b) What is the probability a randomly selected American wants the next president to be middle-aged or willing to compromise but not both? Interpret the result. (c) In a random group of four Americans, what is the probability none of them fell into at least one of the categories? (d) In a random group of six Americans, what is the probability at at most five want the next president to be middle-aged? (e) In a random group of five Americans, what is the probability at least one wants a president that is willing to compromise?

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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Question 1 Please solve with simple probability rules
### Probability and Statistics Exercise **Context:** A poll conducted by Pugh Research resulted in the following findings about Americans' preferences for the next president: - **75%** of Americans want the next president to be middle-aged (35-65 years old). - **57%** prefer a president who is willing to compromise on issues rather than make decisions strictly along partisan lines. - **48%** of the respondents expressed both desires - wanting a middle-aged president who is also willing to compromise. #### Questions: **(a)** What is the probability a randomly selected American wants the next president to be middle-aged or willing to compromise? **(b)** What is the probability a randomly selected American wants the next president to be middle-aged or willing to compromise but not both? **Interpret the result.** **(c)** In a random group of four Americans, what is the probability none of them fell into at least one of the categories? **(d)** In a random group of six Americans, what is the probability at most five want the next president to be middle-aged? **(e)** In a random group of five Americans, what is the probability at least one wants a president that is willing to compromise? **(f)** What is the probability a randomly selected American wants a president willing to compromise given he/she wants the president to be middle-aged? **(g)** Are the events *middle-aged* and *willing to compromise* independent? Justify. --- **Detailed Explanation:** - For questions involving probabilities, consider using probability laws such as the Complement Rule, Addition Rule, and Multiplication Rule. - Conditional probability and the concept of independence will be crucial for parts (f) and (g). - When dealing with questions (c), (d), and (e), the Binomial Distribution may be a helpful tool to model the scenarios.
Transcribed Image Text:### Probability and Statistics Exercise **Context:** A poll conducted by Pugh Research resulted in the following findings about Americans' preferences for the next president: - **75%** of Americans want the next president to be middle-aged (35-65 years old). - **57%** prefer a president who is willing to compromise on issues rather than make decisions strictly along partisan lines. - **48%** of the respondents expressed both desires - wanting a middle-aged president who is also willing to compromise. #### Questions: **(a)** What is the probability a randomly selected American wants the next president to be middle-aged or willing to compromise? **(b)** What is the probability a randomly selected American wants the next president to be middle-aged or willing to compromise but not both? **Interpret the result.** **(c)** In a random group of four Americans, what is the probability none of them fell into at least one of the categories? **(d)** In a random group of six Americans, what is the probability at most five want the next president to be middle-aged? **(e)** In a random group of five Americans, what is the probability at least one wants a president that is willing to compromise? **(f)** What is the probability a randomly selected American wants a president willing to compromise given he/she wants the president to be middle-aged? **(g)** Are the events *middle-aged* and *willing to compromise* independent? Justify. --- **Detailed Explanation:** - For questions involving probabilities, consider using probability laws such as the Complement Rule, Addition Rule, and Multiplication Rule. - Conditional probability and the concept of independence will be crucial for parts (f) and (g). - When dealing with questions (c), (d), and (e), the Binomial Distribution may be a helpful tool to model the scenarios.
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