Final answer:
To calculate the reliability of 5 components in series with an MTBF of 106 hours for a 10-hour operation period, you must first calculate the reliability of a single component and then raise that to the power of 5.
Step-by-step explanation:
The student is asking about the reliability of components in series given a Mean Time Between Failures (MTBF). For components in series, the overall system reliability is the product of the individual reliabilities of each component. First, to find the reliability of a single component with an MTBF of 106 hours over a 10-hour period, we use the exponential reliability function:
R(t) =

For one component over 10 hours:
R(10) =

Once we have the reliability of a single component, we must raise that number to the power of the number of components in series (in this case, 5) to find the overall system reliability, since:
System Reliability =

This yields the answer to the student's question.