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.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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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.
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