Question

A parallel system functions whenever at least one of its components works. Consider a system of 4 components and suppose that each component independently works with probability 0.90. Find the probability that the system functions.

Answer 1

To find the probability that the system functions, we can use the complement rule. The probability that the system functions is 0.9999.

Step-by-step explanation:

To find the probability that the system functions, we can use the complement rule. The complement of the system functioning is the system not functioning. So, the probability of the system not functioning is the probability that all components fail.

Since each component independently works with probability 0.90, the probability that a component fails is 1 - 0.90 = 0.10. Since there are 4 components, the probability that all components fail is 0.10 * 0.10 * 0.10 * 0.10 = 0.0001.

Therefore, the probability that the system functions is 1 - 0.0001 = 0.9999.