What is the probability of system failure for the next year if the battery fails, the AC power fails, and the generator fails?

What is the probability of system failure for the next year if the battery fails, the AC power fails, and the generator fails?

• A. 0.006
• B. 0.06
• C. 0.3
• D. 0.994

Answer: (A)

To determine the probability of system failure in the scenario described, it's vital to consider the dependencies and interrelations between the components mentioned: the battery, the AC power, and the generator. If we assume that these failures are independent events, the total probability of system failure can be calculated by multiplying the probabilities of each individual failure. For example, if the failure probabilities for the battery, AC power, and generator over the next year are provided (let's say P(battery), P(AC power), and P(generator)), the overall probability of system failure would be: \[ P(failure) = P(battery) \times P(AC\ power) \times P(generator) \] In this case, if the calculated probability of failure results in a value of 0.006, it means that the combined effect of the independent failures of these three power sources leads to a low overall likelihood of a system failure. This value emphasizes the robustness of the system design when it includes redundancy (like multiple power sources). When independent components are involved, strategic design can significantly minimize the risk of total system failure even when individual components may have a non-negligible risk. Thus, the answer of 0.006 correctly reflects a very low

To determine the probability of system failure in the scenario described, it's vital to consider the dependencies and interrelations between the components mentioned: the battery, the AC power, and the generator.

If we assume that these failures are independent events, the total probability of system failure can be calculated by multiplying the probabilities of each individual failure. For example, if the failure probabilities for the battery, AC power, and generator over the next year are provided (let's say P(battery), P(AC power), and P(generator)), the overall probability of system failure would be:

[ P(failure) = P(battery) \times P(AC\ power) \times P(generator) ]

In this case, if the calculated probability of failure results in a value of 0.006, it means that the combined effect of the independent failures of these three power sources leads to a low overall likelihood of a system failure.

This value emphasizes the robustness of the system design when it includes redundancy (like multiple power sources). When independent components are involved, strategic design can significantly minimize the risk of total system failure even when individual components may have a non-negligible risk.

Thus, the answer of 0.006 correctly reflects a very low