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Nuclear power plants have redundant components in
Chapter 2, Problem 21E(choose chapter or problem)
Nuclear power plants have redundant components in important systems to reduce the chance of catastrophic failure. Assume that a plant has two gauges to measure the level of coolant in the reactor core and that each gauge has probability 0.01 of failing. Assume that one potential cause of gauge failure is that the electric cables leading from the core to the control room where
the gauges are located may burn up in a fire. Someone wishes to estimate the probability that both gauges fail, and makes the following calculation:
P(both gauges fail) = P(first gauge fails) ×
P(second gauge fails)
= (0.01)(0.01)
= 0.0001
a. What assumption is being made in this calculation?
b. Explain why this assumption is probably not justified in the present case.
c. Is the probability of 0.0001 likely to be too high or too low? Explain.
Image Text Transcription: Nuclear power plants have redundant components in important systems to reduce the chance of catastrophic failure. Assume that a plant has two gauges to measure the level of coolant in the reactor core and that each gauge has probability 0.01 of failing. Assume that one potential cause of gauge failure is that the electric cables leading from the core to the control room where the gauges are located may burn up in a fire. Someone wishes to estimate the probability that both gauges fail, and makes the following calculation: P(both gauges fail) = P(first gauge fails) × P(second gauge fails) = (0.01)(0.01) = 0.0001 a. What assumption is being made in this calculation? b. Explain why this assumption is probably not justified in the present case. c. Is the probability of 0.0001 likely to be too high or too low? Explain.
Questions & Answers
QUESTION:
Nuclear power plants have redundant components in important systems to reduce the chance of catastrophic failure. Assume that a plant has two gauges to measure the level of coolant in the reactor core and that each gauge has probability 0.01 of failing. Assume that one potential cause of gauge failure is that the electric cables leading from the core to the control room where
the gauges are located may burn up in a fire. Someone wishes to estimate the probability that both gauges fail, and makes the following calculation:
P(both gauges fail) = P(first gauge fails) ×
P(second gauge fails)
= (0.01)(0.01)
= 0.0001
a. What assumption is being made in this calculation?
b. Explain why this assumption is probably not justified in the present case.
c. Is the probability of 0.0001 likely to be too high or too low? Explain.
Image Text Transcription: Nuclear power plants have redundant components in important systems to reduce the chance of catastrophic failure. Assume that a plant has two gauges to measure the level of coolant in the reactor core and that each gauge has probability 0.01 of failing. Assume that one potential cause of gauge failure is that the electric cables leading from the core to the control room where the gauges are located may burn up in a fire. Someone wishes to estimate the probability that both gauges fail, and makes the following calculation: P(both gauges fail) = P(first gauge fails) × P(second gauge fails) = (0.01)(0.01) = 0.0001 a. What assumption is being made in this calculation? b. Explain why this assumption is probably not justified in the present case. c. Is the probability of 0.0001 likely to be too high or too low? Explain.
ANSWER:Solution 21E
Step 1 of 3:
We have A Nuclear power plants have redundant components in important systems to reduce the chance of catastrophic failure.To measure the level of coolant in the reactor core the plant has two gauges and probability of each gauge is 0.01 of failing.
Here we are Assuming that one potential cause of gauge failure is that the electric cables leading from the core to the control room where the gauges are located may bum up in a fire. Someone wishes to estimate the probability that both gauges fail, and he makes the following calculation
= (0.01)(0.01)
= 0.0001.
We need to find,
a).We need to write what assumption is being made in this calculation?
b).We need to&n