9. Each of the 4 engines on an airplane functions correctly on a given flight wi
ID: 3303971 • Letter: 9
Question
9. Each of the 4 engines on an airplane functions correctly on a given flight with probability 0.99, and the engines function independently of each other. Below is a table indicating the probability that the plane can make a safe landing under various scenarios: 0 0 (a) What is the probability that only 1 of the engines functions correctly? b) What is the probability that at least 2 of the engines function correctly? (c) What is the probability that the plane makes a safe landing? (d) Given that the flight makes a safe landing, what is the probability that it lands with only 1 of the engines functioning correctly?Explanation / Answer
(a) Probability that an engine functions correctly = 0.99
=> Probability that an engine does not function correctly = 1 - 0.99 = 0.01
There are 4 ways of choosing the correctly functioning engine.
=> Probability that only 1 engine performs correctly = 4 * 0.99 * 0.13
= 0.00000396.
(b) Let us first calculate the probability that no engine functions correctly
= (0.01)4
= 0.00000001
=> Probability that zero or one engine functions correctly
= 0.00000396 + 0.00000001
= 0.00000397
=> Probability that atleast 2 engines function correctly
= 1 - 0.00000397
= 0.99999603.
(c) Probability that the plane makes a safe landing
= 0.00000396 * 0.5 + 0.99999603
= 0.99999801.
(d) Probability that a safely landed plane lands with only 1 engine functioning correctly
= 0.00000396 * 0.5 / 0.99999801
= 0.00000198.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.