4. Related to a job competency exam taken by employees: Of the employees, 24% were males who passed the exam; 36% were females who passed the exam; 16% were males who failed the exam; and 24% were females who failed the exam. Con- sider choosing an employee at random. Let A denote the event that the selected employee passed the exam and M denote the event that the selected employee was male. Are the events A and M independent? (Justify your answer mathe- matically.) What is P(ĀM)?

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4. Related to a job competency exam taken by employees: Of the employees, 24%
were males who passed the exam; 36% were females who passed the exam; 16%
were males who failed the exam; and 24% were females who failed the exam. Con-
sider choosing an employee at random. Let A denote the event that the selected
employee passed the exam and M denote the event that the selected employee
was male. Are the events A and M independent? (Justify your answer mathe-
matically.) What is P(A|M)?
Transcribed Image Text:4. Related to a job competency exam taken by employees: Of the employees, 24% were males who passed the exam; 36% were females who passed the exam; 16% were males who failed the exam; and 24% were females who failed the exam. Con- sider choosing an employee at random. Let A denote the event that the selected employee passed the exam and M denote the event that the selected employee was male. Are the events A and M independent? (Justify your answer mathe- matically.) What is P(A|M)?
Expert Solution
Step 1

Given information:

Notation:

Let

M: Number of male employees.

F: Number of female employees

A: Employees who pass the exam

B: Employees who failed the exam.

So for the simplification make a table of the given information:

Outcome Male (M)  Female (F) Total
Pass (A) 24% 36% 60%
Failed (B) 16% 24% 40%
Total 40% 60% 100%

Find:

1) Event A and M are independent or not.

2) P(A¯|M)

 

Definition:

Independence of two events:

Suppose event A and B are said to be independent if

P(A|B)=P(AB)P(B)=P(A)*P(B)P(B)=P(A)

That is,

P(A|B)=P(A) then event A and B are independent.

 

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