The customer service department of a chimney cleaning company has 3 employees, A

Question

The customer service department of a chimney cleaning company has 3 employees, Arthur, Sarah, and Hank, and each works from the office part of the time and from home part of time independently from one another. If Arthur works from the office 75% of the time, Sarah works from the office 70% of the time, and Hank works from the office 40% of the time, what is the probability that on any given day:

a) Hank will be working from the office and Arthur will be working from home?

b) All of them will be working from the office?

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

Explanation / Answer

Let

A = arthur is in office
S = sarah is in office
H = hank is in office

a)

As they are independent,

P(H n A') = P(H) P(A') = 0.40*(1-0.75) = 0.10 [ANSWER]

******************

b)
As they are independent,

P(A n S n H) = P(A) P(S) P(H) = 0.75*0.70*0.40 = 0.21 [ANSWER]

******************

c)

P(at least one not at home) = 1 - P(no one is at home)

= 1 - P(all at office)

= 1 - P(A n S n H)

= 1 - 0.21

= 0.79 [ANSWER[

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