Question

In airline​ applications, failure of a component can result in catastrophe. As a​ result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.0072 and the system that utilizes the component is part of a triple modular redundancy. ​(a) Assuming each​ component's failure/success is independent of the​ others, what is the probability all three components​ fail, resulting in disaster for the​ flight? ​(b) What is the probability at least one of the components does not​ fail?

Answer 1

Answer:

(a) 0.000000373248

(b) 0.999999626752

Step-by-step explanation:

The aircraft works when at least one of its components works

Probability of failure, f=0.0072

Probability of success, s=1-0.0072=0.9928

(a)

P(all three components fail)=$f^{3}$

probability=$0.0072^{3}$=0.000000373248

(b)

Probability (at least one of the components does not​ fail)=1-P(all three components fail)

Probability=$1-0.0072^{3}$

Probability=1-0.000000373248=0.999999626752