(Solved): Please Help..Thx (10 points) A network of switches \( a, b, c, d \) is connected across two power ...

Please Help..Thx

(10 points) A network of switches \( a, b, c, d \) is connected across two power lines \( A \) and \( B \) (see Figure 1). Assume the switches are electronically controlled and all activated at the same time. When a switch is activated, the probability that it will NOT close is \( p \). (a) (2 points) What is the probability that the circuit between \( A \) and \( B \) will fail to close? (b) (4 points) If a line connecting the two switch lines is added at \( e \), what is the probability that the circuit between \( A \) and \( B \) will fail to close? (c) (4 points) If a line and an additional switch is added at \( e \), what is the probability that the circuit between \( A \) and \( B \) will fail to close?