Nuclear power plants have redundant components in important systems to reduce the chance of catastrophic failure. Suppose that a plant has three gauges to measure the level of the coolant in the reactor core and each gauge has a 0.02 probability of failing. What is the probability that none of the gauges fails

0.9412 = 94.12% probability that none of the gauges fails

Step-by-step explanation:

For each gauge, there are only two possible outcomes. Either it fails, or it does not. The probability of a gauge failing is independent of other gauges. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

3 gouges, each with a 0.02 probability of failing.

This means that

What is the probability that none of the gauges fails?

This is P(X = 0).

0.9412 = 94.12% probability that none of the gauges fails

nope.   happens to me as well.

-aparri

x = 12

y = 1

for the points!