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
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
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.
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**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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