An electric circuit includes a device that gives energy to the charged particles constituting the current, such as a battery or a generator; devices that use current, such as lamps, electric motors, or computers; and the connecting wires or transmission lines.; an electric circuit consists of two subsystems say a and b as shown below:; for previous testing procedures, the following probabilities are assumed to be known.; p(a fails) = 0.2, p(b fails alone) = 0.15, p(a and b fail) = 0.15; based on the above information answer the following questions:
(a) what is the probability that b fails?
(b) what is the probability that a fails alone?
(c) find the probability that the whole of the electric system fails?; or; find the conditional probability that b fails when a has already failed.