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?