Concept explainers
Management: The Bureau of Labor Statistics reported that 64.5 trillion women and 74.6 men were employed. Of the women. 25.8 million had management jobs, and of the men, 25.0 million had management jobs. An employed person is chosen at random.
What is the probability that the person is a female?
What is the probability that the person has a management job?
What is the probability that the person is female and has a management job?
Given that the person is female, what is the probability that she has a management job?
Given that the person has a management job, what is due probability that the person is female?
(a)
The probability that randomly chosen person is female.
Answer to Problem 44E
Explanation of Solution
Given:
Total number of female is 64.5 million and male is 74.6 million.
Number of person with management job from women is 25.8 million and that of men is 25.0.
Formula Used:
Probability of an event is given by
Calculation:
Let
Hence, the probability that randomly chosen person is female,is
(b)
The probability that randomly chosen person has management job.
Answer to Problem 44E
Explanation of Solution
Given:
Total number of female is 64.5 million and male is 74.6 million.
Number of person with management job from women is 25.8 million and that of men is 25.0.
Formula Used:
Probability of an event is given by
Calculation:
Let
Hence, the probability that randomly chosen person has management job is,
(c)
The probability that the chosen one is femle and has management job.
Answer to Problem 44E
Explanation of Solution
Given:
Total number of female is 64.5 million and male is 74.6 million.
Number of person with management job from women is 25.8 million and that of men is 25.0.
Formula Used:
For any two t events
Calculation:
Let
Let
So,
There are 25.8 millionfemale who has management job.
The probability that selected one is femle and has management jobis,
(d)
The probability that a person has management job, given that person is female.
Answer to Problem 44E
Explanation of Solution
Given:
Total number of female is 64.5 million and male is 74.6 million.
Number of person with management job from women is 25.8 million and that of men is 25.0.
Formula Used:
For any two dependent events
Where
Calculation:
Let
Let
So,
There are 25.8 millionfemale who has management job.
Therefore,
So, the probability of the event “a person has management job, given that person is female” is calculated as follows:
The probability thata person has management job, given that person is femaleis,
(e)
The probability that a person is female, given that person has management job.
Answer to Problem 44E
Explanation of Solution
Given:
Total number of female is 64.5 million and male is 74.6 million.
Number of person with management job from women is 25.8 million and that of men is 25.0.
Formula Used:
For any two dependent events
Where
Calculation:
Let
Let
So,
There are 25.8 millionfemale who has management job.
Therefore,
So, the probability of the event “a person is female, given that person has management job” is calculated as follows:
The probability thata person is female, given that person has management jobis,
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Chapter 5 Solutions
Elementary Statistics
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