The switch network shown in Figure P1.53 represents a digital communication link. Switches , i = 1, . . . , 6, are open or closed and operate independently. The probability that a switch is closed is p. Let represent the event that switch is closed. (a) In terms of the Ai’s write the event that there exists at least one closed path from 1 to 2. (b) Compute the probability of there being at least one closed path from 1 to 2.