The number N of devices that a technician must try to repair during the course of an arbitrary workday is a random variable having a geometric distribution with parameter p = 1/8. We estimate the probability that he manages to repair a given device to be equal to 0.95, independently from one device to another.

1. What is the probability that the technician manages to repair exactly five devices, before his second failure, during a given workday, if we assume that he will receive at least seven out-of-order devices in the course of this particular workday?
2. If, in the course of a given workday, the technician received exactly ten devices for repair, what is the probability he managed to repair exactly eight of those?
3. Use a Poisson distribution to calculate approximately the probability in part (b).
4. Suppose that exactly eight of the ten devices in part (2) have indeed been repaired. If we take three devices at random and without replacement among the ten that the technician had to repair, what is the probabiliyu that the two devices he could not repair are among those?