# Question

A commercial jet aircraft has four engines. For an aircraft in flight to land safely, at least two engines should be in working condition. Each engine has an independent reliability of p = 92%.

a. What is the probability that an aircraft in flight can land safely?

b. If the probability of landing safely must be at least 99.5%, what is the minimum value for p? Repeat the question for probability of landing safely to be 99.9%.

c. If the reliability cannot be improved beyond 92% but the number of engines in a plane can be increased, what is the minimum number of engines that would achieve at least 99.5% probability of landing safely? Repeat for 99.9% probability.

d. One would certainly desire 99.9% probability of landing safely. Looking at the answers to (b) and (c), what would you say is a better approach to safety, increasing the number of engines or increasing the reliability of each engine?

a. What is the probability that an aircraft in flight can land safely?

b. If the probability of landing safely must be at least 99.5%, what is the minimum value for p? Repeat the question for probability of landing safely to be 99.9%.

c. If the reliability cannot be improved beyond 92% but the number of engines in a plane can be increased, what is the minimum number of engines that would achieve at least 99.5% probability of landing safely? Repeat for 99.9% probability.

d. One would certainly desire 99.9% probability of landing safely. Looking at the answers to (b) and (c), what would you say is a better approach to safety, increasing the number of engines or increasing the reliability of each engine?

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