5.51 Failure and repair of photocopiers In a photocopy center, there are two small photocopiers, two medium photocopiers and one big photocopier. The probability that a small one fails and requires repairs is 0.1, a medium one fails and requires repairs is 0.08, and the probability that the big photocopier fails and requires repairs is 0.05.

Assume that all five copiers operate independently.

a. What is the probability that all the photocopiers fail and require repairs?

b. What is the probability that none of the photocopiers fails and requires repairs?

c. What is the probability that one of the photocopiers fails and requires repairs?

d. What is the probability that one of the small photocopiers fails and requires repairs?

e. What is the probability that at least one of the five copiers fails and requires repairs?