In the circuit diagram given below, P(Switch # i is open) = P, i = 1,2,3. It is assumed that three switches are opened and closed independently of each other with their probabilities. If 2 switches are closed together with any other switch or if only 2 switches are closed, electricity will not be transmitted at all. If switch 3 and 1 are closed together, no electricity is transmitted. There are conditions: If only 1 switch is closed, electricity is transmitted and If only 3 switches are closed, electricity is transmitted.

a) Calculate the probability of transmitting electric current from A to B.

b) If p1 = p2 = p3 = p, what can be said about the probabilities in a).

c) If p1 = 0.90, p2 = 0.95, p = 0.99, what can be said about the probabilities in a) and b).