10. A network of switches a, b, c, and d is connected across the pow the sketch. Assume that the switches operate electrically and have i mechanisms. All are controlled simultaneously by the same impulses on an impulse all switches shall close simultaneously. But each switc failure (it will not close when it should).

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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).
A
a
C
de
Power lines
b
d
B
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?
Transcribed Image Text: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). A a C de Power lines b d B 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?
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