Question

A certain electronic system contains 10 components. Suppose that the probability that each individual component will fail is 0.2 and that the components fail independently. What is the probability that at least one component will not fail?

Answer 1

The probability that at least one component will not fail is approximately 89.26%.

Step-by-step explanation:

To find the probability that at least one component will not fail, we can find the complement of the probability that all components will fail. Since each component has a probability of 0.2 of failing, the probability that a component will not fail is 1 - 0.2 = 0.8. Since the components fail independently, the probability that all 10 components will fail is (0.2)^10. Therefore, the probability that at least one component will not fail is 1 - (0.2)^10 = 0.8926, or approximately 89.26%.