The customer service department of a chimney cleaning company has 4 employees, S

Question

The customer service department of a chimney cleaning company has 4 employees, Scott, Carrie, Alan, and Michelle, and each works from the office part of the time and from home part of time independently from one another. If Scott works from the office 80% of the time, Carrie works from the office 85% of the time, Alan works from the office 70% of the time, and Michelle works from the office 55% of the time, what is the probability that on any given day:

a) Carrie will be working from the office and Michelle will be working from home?

b) All of them will be working from home?

c) At least one of them will not be working from the office?

Explanation / Answer

a)

P = P(carrie office) P(michelle home)

P = (0.85)*(1-0.55) = 0.3825 [ANSWER]

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B)

p(all home) = (1-0.80)*(1-0.85)*(1-0.70)*(1-0.55) = 0.00405 [ANSWER]

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c)

P(at least one not office) = 1 - P(all office)

= 1 - 0.80*0.85*0.70*0.55

= 0.7382 [ANSWER]

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