Question

10. The principle of redundancy is used when system reliability is improved through redundant or backup components. A​ region's government requires that commercial aircraft used for flying in hazardous conditions must have two independent radios instead of one. Assume that for a typical​ flight, the probability of a radio failure is 0.0037. What is the probability that a particular flight will be threatened with the failure of both​radios? Describe how the second independent radio increases safety in this case.

What is the probability that a particular flight will be threatened with the failure of both​ radios?

_____​(Round to six decimal places as​ needed.)

Describe how the second independent radio increases safety in this case. Choose the correct answer below.

A. The second radio has no effect on safety.

B. With one radio there is a 0.0037 probability of a serious​ problem, but with two independent​ radios, the probability of a serious problem increases substantially. The flight becomes much less safe with two independent radios.

C. With one radio there is a 0.0037 probability of a serious​ problem, but with two independent​ radios, the probability of a serious problem decreases substantially. The flight becomes much safer with two independent radios.

D. The second radio makes it impossible for the airplane to crash

Answer 1

Solution:

What is the probability that a particular flight will be threatened with the failure of both radios?

Answer: We are given that the probability of a radio failure is 0.0037.

We are also given that the two independent radio's installed are independent.

Therefore, the probability that a particular flight will be threatened with the failure of both​ radios is

Describe how the second independent radio increases safety in this case.

Answer: C. With one radio there is a 0.0037 probability of a serious​ problem, but with two independent​ radios, the probability of a serious problem decreases substantially. The flight becomes much safer with two independent radios.