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Probability: black-and-white and color copiers

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A local FedEx/Kinkos has three black-and-white copy machines and two color copiers. Based on historical data, the chances that each black-and-white copier will be down for repairs is 0.10. The color copiers are more of a problem and are down 20% of the time each.

a. Based on this information, what is the probability that if a customer needs a color copy, both color machines will be down for repairs?

b. If a customer wants both a color copy and a black and-white copy, what is the probability that the necessary machines will be available? (Assume that the color copier can also be used to make a black-and-white copy if needed.)

c. If the manager wants to have at least a 99% chance of being able to furnish a black-and-white copy on demand, is the present configuration sufficient? (Assume that the color copier can also be used to make a black-and-white copy if needed.) Back up your answer with appropriate probability computations.

d. What is the probability that all five copiers will be up and running at the same time? Suppose the manager added a fourth black-and-white copier, how would the probability of all copiers being ready at any one time is affected?

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a)
P(both color copiers are down)
= (.2)(.2)
= 0.04

b)
P(at least one color copier available)
= 1 - P(both color copiers down)
= 1 - 0.04
= 0.96

c)
P(at least one ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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