What is the probability of success for a system with a failure probability of 0.01 over a twenty-year mission?

What is the probability of success for a system with a failure probability of 0.01 over a twenty-year mission?

• A. 0.8
• B. 0.818
• C. 0.2
• D. 0.892

Answer: (B)

To determine the probability of success for a system with a given failure probability over a mission duration, we utilize the concept of reliability. When given a failure probability of 0.01, this indicates a 1% chance of failure during the mission period. Thus, the probability of the system successfully completing the mission is represented as the complementary probability of failure. The calculation for the success probability over a twenty-year mission involves defining the overall probability of the system not failing during this period. If we denote the failure probability as p (0.01 in this case), then the probability of success (not failing) for each year can be expressed as 1 - p, or 0.99. To find the overall success probability over twenty years, we would raise the per-year success probability to the power of the number of years, which would be calculated as follows: \[ P(success) = (1 - p)^{n} = (0.99)^{20} \] Upon performing the calculation, this results in: \[ P(success) = (0.99)^{20} \approx 0.818 \] This effectively means that there’s about an 81.8% chance that the system will successfully

To determine the probability of success for a system with a given failure probability over a mission duration, we utilize the concept of reliability. When given a failure probability of 0.01, this indicates a 1% chance of failure during the mission period. Thus, the probability of the system successfully completing the mission is represented as the complementary probability of failure.

The calculation for the success probability over a twenty-year mission involves defining the overall probability of the system not failing during this period. If we denote the failure probability as p (0.01 in this case), then the probability of success (not failing) for each year can be expressed as 1 - p, or 0.99. To find the overall success probability over twenty years, we would raise the per-year success probability to the power of the number of years, which would be calculated as follows:

[

P(success) = (1 - p)^{n} = (0.99)^{20}

]

Upon performing the calculation, this results in:

[

P(success) = (0.99)^{20} \approx 0.818

]

This effectively means that there’s about an 81.8% chance that the system will successfully