Problem 2 (20 points) For a certain population of employees, the percentage passing or failing a job competency exam, listed according to sex, were as shown in the accompanying table. That is, of all the people taking the exam, 15% were in the male-pass category, 25% were in the male-fail category, and so forth. An employee is to be selected randomly from this population. Let A be the event that the employee scores a passing grade on the exam and let M be the event that a male is selected. Outcome Male (M) Female (F) Total Pass 15 35 50 Fail 20 30 50 Total 35 65 100 1. Are the events Pass and Male independent? 2. Are the events Fail and Female independent? 3. What is the probability that you pass given that you are a male P(Pass | Male)?

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Problem 2 (20 points)
For a certain population of employees, the percentage passing or failing a job competency
exam, listed according to sex, were as shown in the accompanying table. That is, of all the
people taking the exam, 15% were in the male-pass category, 25% were in the male-fail
category, and so forth. An employee is to be selected randomly from this population. Let A be
the event that the employee scores a passing grade on the exam and let M be the event that a
male is selected.
Outcome
Male (M) Female (F) Total
Pass
15
35
50
Fail
20
30
50
Total
35
65
100
1. Are the events Pass and Male independent?
2. Are the events Fail and Female independent?
3. What is the probability that you pass given that you are a male P(Pass | Male)?
Transcribed Image Text:Problem 2 (20 points) For a certain population of employees, the percentage passing or failing a job competency exam, listed according to sex, were as shown in the accompanying table. That is, of all the people taking the exam, 15% were in the male-pass category, 25% were in the male-fail category, and so forth. An employee is to be selected randomly from this population. Let A be the event that the employee scores a passing grade on the exam and let M be the event that a male is selected. Outcome Male (M) Female (F) Total Pass 15 35 50 Fail 20 30 50 Total 35 65 100 1. Are the events Pass and Male independent? 2. Are the events Fail and Female independent? 3. What is the probability that you pass given that you are a male P(Pass | Male)?
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