A device has N similar components which may fail independently, with probability p of failure of any component. The device fails if one or more of the components fails. In the event of failure of the device, the components are tested sequentially.
- What is the probability the first defective unit tested is the nth, given one or more components have failed?
- What is the probability the defective unit is the nth, given that exactly one has failed?
- What is the probability that more than one unit has failed, given that the first defective unit is the nth?
Pfeiffer, Applied Probability, 4.4 Problems on Independence of Events, exercise 50