The number N of devices that a technician must try to repairduring the course of an arbitrary workday is a random variablehaving a geometric distribution with parameter p = 1/8. We estimatethe probability that he manages to repair a given device to beequal to 0.95, independently from one device to another
a) What is the probability that the technician manages to repairexactly five devices, before his second failure, during a givenworkday, if we assume that he will receive at least sevenout-of-order devices in the course of this particular workday?
b) If, in the course of a given workday, the technician receivedexactly ten devices for repair, what is the probability that hemanaged to repair exactly eight of those?
c) Use a Poisson distribution to calculate approximately theprobability in part (b).
d) Suppose that exactly eight of the ten devices in part (b)have indeed been repaired. If we take three devices at random andwithout replacement among the ten that the technician had torepair, what is the probability that the two devices he could notrepair are among those?
