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?

The probability the all three components fail and that atleast one of the component does not fail is :

The probability of failure of each component is given as :

The probability that all 3 components fail can be expressed thus :

P(all 3 fail) = P(failure) × P(Failure) × P(Failure)

P(all 3 fail) = 0.0072 × 0.0072 × 0.0072 = 0.000000373248

The probability that atleast one of the components does not fail is :

P(Atleast 1 does not fail) = 1 - P(all 3 fail)

P(Atleast 1 does not fail) = 1 - 0.000000373248

P(Atleast 1 does not fail) = 0.999999626752

Therefore, the probabilities that all 3 fail and that atleast one does not fail are 0.000000373248 and 0.999999626752

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(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)=

probability==0.000000373248

(b)

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

Probability=

Probability=1-0.000000373248=0.999999626752

b.my answer is b.

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