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 inde- pendent reliability of p  92%. a. What is the probability that an aircraft in flight can land safely?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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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 inde-
pendent 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 mini-
mum 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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