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 bum up in a fire. Someone wishes to estimate the probability that both gauges fail, and makes the following calculation:

P (both gauge fail) = P(first guage fails) × P (Second guage 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.

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 Explain why this assumption is probably not justified in the present case.

c).We need to check Is the probability of 0.0001 likely to be too high or too low? Explain.

Step2 of 3:

a).

In this calculation we made an assumption that the gauges fail independently.

b).

This assumption is probably not justified in the present case because, One cause of failure and a fire, will cause both gauges to fail.

Therefore, they do not fail independently.

Step3 of 3:

c).

The probability of 0.0001 likely “Too Low” because, probability value is near to 0 and also we can say that there is chance that both gauges fail together in a fire so, the condition that the first gauge fails makes it more likely that the second gauge fails.

Hence, the correct calculation would be

Therefore,