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:

Question

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 1

(a) That the gauges fail independently.

(b) One cause of failure, a fire, will cause both gauges to fail. Therefore, they do not fail independently.

(c) Too low. The correct calculation would use P(second gauge fails|first gauge fails) in place of P(second gauge fails).
Because there is a chance that both gauges fail together in a fire, the condition that the first gauge fails makes it more likely that the second gauge fails as well.
Therefore P(second gauge fails|first gauge fails) > P(second gauge fails).