The AAA system contains 3 independent components in parallel, each with probability of failure 0.4. Find the expected number of systems inspected until the first failed unit.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either it fails, or it does not. The components are independent. We want to know how many outcomes until r failures. The expected value is given by

In which r is the number of failures we want and p is the probability of a failure.

In this problem, we have that:

r = 1 because we want the first failed unit.

The expected number of systems inspected until the first failed unit is 2.5