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As of January 3, 2019, the US House of Representatives had the following demographics: U.S. House of Representatives Gender 183 144 15 91 198 235 Source: U.S. House of Representatives Press Gallery. Recall that two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. We also define this as P(B|A)=P(B) Political Party Republican Democrat Total 327 106 433 Male Female Total 1. Without doing any calculations, do you feel that the events of Political Party and Gender are independent? In other words, do you feel as though the probability of political party influences the probability of Gender? Explain your reasoning. 2. How we feel about independence is not enough. Let's look at an example of testing independence using our equation P(B|A)=P(B). Let the event A be a male and let event B be a Republican. a. Find the probability that a randomly selected member of the U.S. House of Representative is Republican given that they are a male? This is P(B|A). b. Find the probability that a randomly selected member of the U.S. House of Representative is Republican? This is P(B). c. Does your answer in part a equal your answer in part b? If yes, then the events are independent. If no, then the events are dependent.

As of January 3, 2019, the US House of Representatives had the following demographics: U.S. House of Representatives Gender 183 144 15 91 198 235 Source: U.S. House of Representatives Press Gallery. Recall that two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. We also define this as P(B|A)=P(B) Political Party Republican Democrat Total 327 106 433 Male Female Total 1. Without doing any calculations, do you feel that the events of Political Party and Gender are independent? In other words, do you feel as though the probability of political party influences the probability of Gender? Explain your reasoning. 2. How we feel about independence is not enough. Let's look at an example of testing independence using our equation P(B|A)=P(B). Let the event A be a male and let event B be a Republican. a. Find the probability that a randomly selected member of the U.S. House of Representative is Republican given that they are a male? This is P(B|A). b. Find the probability that a randomly selected member of the U.S. House of Representative is Republican? This is P(B). c. Does your answer in part a equal your answer in part b? If yes, then the events are independent. If no, then the events are dependent.

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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As of January 3, 2019, the US House of Representatives had the following demographics: U.S. House of Representatives Gender 183 15 198 Source: U.S. House of Representatives Press Gallery. Recall that two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. We also define this as P(B|A)- P(B) Political Party Republican Democrat Total 327 106 433 Male Female Total 144 91 235 ¸ 1. Without doing any calculations, do you feel that the events of Political Party and Gender are independent? In other words, do you feel as though the probability of political party influences the probability of Gender? Explain your reasoning. 2. How we feel about independence is not enough. Let's look at an example of testing independence using our equation P(B|A)=P(B). Let the event A be a male and let event B be a Republican. a. Find the probability that a randomly selected member of the U.S. House of Representative is Republican given that they are a male? This is P(B|A) b. Find the probability that a randomly selected member of the U.S. House of Representative is Republican? This is P(B). c. Does your answer in part a equal your answer in part b? If yes, then the events are independent. If no, then the events are dependent.
Transcribed Image Text:As of January 3, 2019, the US House of Representatives had the following demographics: U.S. House of Representatives Gender 183 15 198 Source: U.S. House of Representatives Press Gallery. Recall that two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. We also define this as P(B|A)- P(B) Political Party Republican Democrat Total 327 106 433 Male Female Total 144 91 235 ¸ 1. Without doing any calculations, do you feel that the events of Political Party and Gender are independent? In other words, do you feel as though the probability of political party influences the probability of Gender? Explain your reasoning. 2. How we feel about independence is not enough. Let's look at an example of testing independence using our equation P(B|A)=P(B). Let the event A be a male and let event B be a Republican. a. Find the probability that a randomly selected member of the U.S. House of Representative is Republican given that they are a male? This is P(B|A) b. Find the probability that a randomly selected member of the U.S. House of Representative is Republican? This is P(B). c. Does your answer in part a equal your answer in part b? If yes, then the events are independent. If no, then the events are dependent.
Expert Solution
Step 1

Given that,

    Political Party  
    Republican (B) Democrat (B') Total
Gender Male (A) 183 144 327
  Female (A') 15 91 106
  Total 198 235 433

 

 

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