A machine produces components for use in cellular phones. At any given time, the machine may be in one, and only one, of three states: operational, out of control, or down. From experience with this machine, a quality control engineer knows that the probability that the machine is out of control at any moment is 0.02, and the probability that it is down is 0.015.
a. What is the relationship between the two events "machine is out of control" and "machine is down"?
b. When the machine is either out of control or down, a repair person must be called. What is the probability that a repair person must be called right now?
c. Unless the machine is down, it can be used to produce a single item. What is the probability that the machine can be used to produce a single component right now? What is the relationship between this event and the event "machine is down"?