Concept explainers
U.S. senators: The following table displays the 100 senators of the 113th U.S. Congress on January 3, 2013. Viewed by political party affiliation and gender.
A senator is selected at random from this group.
- What is the
probability that the senator is a woman? - What is the probability that the senator is a Republican?
- What is the probability that the senator is a Republican and a woman?
- Given that the senator is a woman, what is the probability that she is a Republican?
- Given that the senator is a Republican. what is the probability that the senator is a woman?
(a)
The probability that randomly chosen senator is a women.
Answer to Problem 40E
Explanation of Solution
Given:
The following table categorizes 100 senator individuals.
Male | Female | Total | |
Democrat | 36 | 16 | 52 |
Republican | 42 | 4 | 46 |
Independent | 2 | 0 | 2 |
Total | 80 | 20 | 100 |
Formula Used:
Probability of an event is given by
Calculation:
Let
Hence, the probability of the event that randomly chosen senator is a woman,is
(b)
The probability that randomly chosen senator is Republican.
Answer to Problem 40E
Explanation of Solution
Given:
The following table categorizes 100 senator individuals.
Male | Female | Total | |
Democrat | 36 | 16 | 52 |
Republican | 42 | 4 | 46 |
Independent | 2 | 0 | 2 |
Total | 80 | 20 | 100 |
Formula Used:
Probability of an event is given by
Calculation:
Let
Hence, the probability of the event that randomly chosen senator is a republican, is
(c)
The probability that the senator is republican and women.
Answer to Problem 40E
Explanation of Solution
Given:
The following table categorizes 100 senator individuals.
Male | Female | Total | |
Democrat | 36 | 16 | 52 |
Republican | 42 | 4 | 46 |
Independent | 2 | 0 | 2 |
Total | 80 | 20 | 100 |
Formula Used:
For any two t events
Calculation:
Let
Let
So,
There are 4 women who are Republican.
The probability that the senator is republican and women, is
(d)
The probability to a senator of being republican, given that she is woman.
Answer to Problem 40E
Explanation of Solution
Given:
The following table categorizes 100 senator individuals.
Male | Female | Total | |
Democrat | 36 | 16 | 52 |
Republican | 42 | 4 | 46 |
Independent | 2 | 0 | 2 |
Total | 80 | 20 | 100 |
Formula Used:
For any two dependent events
Where
Calculation:
Let
Let
So,
There are 4 women who are Republican.
Therefore,
So, the probability of the event “a senator of being republican, given that she is woman” is calculated as follows:
The probability to a senator of being republican, given that she is woman is
(e)
The probability to a senator of being woman, given that individual is republican.
Answer to Problem 40E
Explanation of Solution
Given:
The following table categorizes 100 senator individuals.
Male | Female | Total | |
Democrat | 36 | 16 | 52 |
Republican | 42 | 4 | 46 |
Independent | 2 | 0 | 2 |
Total | 80 | 20 | 100 |
Formula Used:
For any two dependent events
Where
Calculation:
Let
Let
So,
There are 4 women who are Republican.
Therefore,
So, the probability of the event “a senator of being republican, given that she is woman” is calculated as follows:
The probability to a senator of being woman, given that individual is republican is
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Chapter 5 Solutions
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