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Old 09-17-2018, 08:33 PM
jchaney jchaney is offline
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Default Custom Problem of My Own

Assumptions:
There are 20 work days in the month.
An employee has a maximum of three additional days sick time per month.
Sick days are uniformly likely on any given day.

What is the probability that an employee calls out the first two 'Saturdays' of each month three months in a row?

Help me wrap my mind about how to set this up.

Week 1 (5c1)*(3/20)*(17/20)^4 = .3915
Week 2 (5c1)*(3/20)*(17/20)^4 = .3915*(same day of week 1/5)= .0783
Week 3 (5c0)*(17/20)^5=.4437
Week 4 (5c0)*(17/20)^5=.4437

Probability for one month: .3915*.0783*.4437^2=.006

Probability for three months: .006^3=.000000219
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Old 09-18-2018, 11:44 AM
ARodOmaha ARodOmaha is offline
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Quote:
Originally Posted by jchaney View Post
Assumptions:
There are 20 work days in the month.
An employee has a maximum of three additional days sick time per month.
Sick days are uniformly likely on any given day.

What is the probability that an employee calls out the first two 'Saturdays' of each month three months in a row?

Help me wrap my mind about how to set this up.

Week 1 (5c1)*(3/20)*(17/20)^4 = .3915
Week 2 (5c1)*(3/20)*(17/20)^4 = .3915*(same day of week 1/5)= .0783
Week 3 (5c0)*(17/20)^5=.4437
Week 4 (5c0)*(17/20)^5=.4437

Probability for one month: .3915*.0783*.4437^2=.006

Probability for three months: .006^3=.000000219
Couple questions: (1) Are you assuming that Saturday is a work day? If it isn't a work day, then the employee wouldn't call in, so the probability is zero. If the employee is calling in on their day off, they should reexamine their education. (2) What do you mean the employee has "three additional work days"? No clue what you mean by "additional."

I would stick to questions that are clearly defined and don't work with ambiguous numbers of days in the month and number of weeks in the month.
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Old 09-18-2018, 01:44 PM
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Gandalf Gandalf is offline
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I agree. Better to stick with well-defined questions. Here, itís questionable why if the binomial distribution is appropriate at all, if there is a maximum of 3 call-ins per month (and also a minimum of 3? Otherwise why is 3/20 appropriate?). And why is it less likely that a call-in is Saturday the first week than the second?
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