Relays used in the construction of electric circuits function properly with prob

Question

Relays used in the construction of electric circuits function properly with probability .9. Assuming that the circuits operate independently, which of the following circuit designs yields the higher probability that current will flow when the relays are activated? Refer to Exercise 2.163 and consider circuit A. If we know that current is flowing, what is the probability that switches 1 and 4 are functioning properly? Refer to Exercise 2.163 and consider circuit B. If we know that current is flowing, what is the probability that switches 1 and 4 are functioning properly?

Explanation / Answer

2.163: So let's determine the probability of diagram A. The currentcan either flow using 1 and 3, 1 and 4, 2 and 3, or 2 and4. Diagram B: The current can flow using either 1 and 3, or 2 and4. So the probability for diagram A is: 1 - [(1 - .9) ^ 4] =.9987 Probability of diagram B: 1 - [(1 - .9) ^ 2] =.9639 So Diagram A is more likely to work.

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