10. A network of switches a, b, c, and d is connected across the power lines A and B as shown in the sketch. Assume that the switches operate electrically and have independent operating mechanisms. All are controlled simultaneously by the same impulses; that is, it is intended that on an impulse all switches shall close simultaneously. But each switch has a probability p of failure (it will not close when it should). b A e B C d Power lines a. What is the probability that the circuit from A to B will fail to close? b. If a line is added on at e, as indicated in the sketch, what is the probability that the circuit from A to B will fail to close? c. If a line and switch are added at e, what is the probability that the circuit from A to B will fail to close