The customer service department of a costume manufacturing c

The customer service department of a costume manufacturing company has 3 employees, Jack, Sally, and Zero, and each works from the office part of the time and from home part of time independently from one another. If Jack works from the office 70% of the time, Sally works from the office 45% of the time, and Zero works from the office 90% of the time, what is the probability that on any given day: Zero will be working from the office and Sally will be working from home? All of them will be working from the office? At least one of them will not be working from home?

Solution

When two events, A and B, are independent, the probability of both occurring is:

Zero : working from home = 0.1

   working from offfice = 0.9

Sally : working from home = 0.55

   working from offfice = 0.45

Jack : working from home = 0.3

   working from offfice = 0.7

a) Zero from office and Sally from home = 0.9*0.55 = 0.495

b) All three working from office = 0.9*0.45*0.7 = 0.2835

c) At least one of them is not working from home:

1 one of them not working from home : 0.1*0.55*0.7 + 0.1*0.45*0.3 + 0.9*0.55*0.33 = 0.21535

2 of them not working from home : 0.9*0.45*0.3 + 0.9*0.7*0.55 + 0.1*0.45*0.55 = 0.49275

3 of them not working from home : 0.2835

Probability of atleast 1 not working from home = 0.21535+0.49275 +0.2835 = 0.9916

	P(A and B) = P(A) · P(B)