Suppose that we have a communication system that employs ten transmitters. So long as at least nine of ten transmitters are functioning, the system will work. If more than one transmitter is not functioning, the system will not work. Suppose that at any given time, there is a probability 0.1 that a transmitter will not be functioning. Assume that each transmitter behaves independently of the other transmitters.
a) Determine the probability that the system will be working at any given time?
b) You are inspecting the system to determine whether any transmitters need to be replaced. What is the probability that you will find one or more of the transmitters need to be replaced?