Question

Question 4. Consider the electrical circuit depicted below. Current will flow from a to b if there is at least one closed path when the relays are switched to "closed". However, the relays may malfunction. Suppose the probability that the three relays depicted below close properly are: Pi = 0.9, P2 = 0.85 and P3 = 0.95, respectively. All relays operate independently of each other and are mutually independent as well. Let A denote the event that current will flow from a to b when all relays are switched to "closed". a) Compute P(A) b) Compute the probability that if the current is flowing, relay 1 has closed (i.e. functioning properly). c) Compute the probability that if the current is flowing, relay 3 is open (i.e. malfunctioning).

Answer 1

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= 0.9 @ P ( A gives that relay 3 is open ) . P (A not moking) epf an is not cooking Topfo is not working a sum of probability of inod cace tuh ease alle case. = 0.1ox0.8570.05+0.9000 157 +0.90x 0.85X0.05 € 0.049 at We had used, 0 şi with probability to with probability 0.90 0.10- it to and - Similarly, we applied

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