SOLUTION: The personnel manager of a manufacturing company has cross-classified the 400 employees of his company according to their record of absenteeism last year, and whether or not they w
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Question 1019204: The personnel manager of a manufacturing company has cross-classified the 400 employees of his company according to their record of absenteeism last year, and whether or not they were smokers, as shown in the following table.
Number of days absent Smoker Nonsmoker
Less than 10 34 260
10 or more 78 28
If one of these employees is selected at random.
a. What is the probability that the employee selected was a non-smoker?
b. What is the probability that the employee selected was absent for 10 or more days?
c. Are the events “non-smoker” and “absent less than 10 days” mutually exclusive? Explain.
d. What is the probability that the employee selected was absent for less than 10 days given that the employee is a smoker?
e. What is the probability that the employee selected was absent for less than 10 days given that the employee does not smoke?
You can put this solution on YOUR website! a. (28+260)/400 = 18/25
b. (78+28)/400 = 53/200
c. The two events are mutually exclusive if P("non-smoker" and "absent less than 10 days") = 0. Since from the data, P("non-smoker" and "absent less than 10 days") = 260/400 = 13/20, the two events are NOT mutually exclusive.
d. P("absent for less than 10 days"|smoker) = P("absent for less than 10 days" AND smoker)/P(smoker) =
e. P("absent for less than 10 days"|non-smoker) = P("absent for less than 10 days" AND non-smoker)/P(non-smoker) =
