Question

3) An airplane has 2 engines. P(malfunction) = .0004 for a single engine on a single flight and these malfunctions are independent. A flight will crash if both engines malfunction on that flight. The plane makes 3 roundtrips per day [which is 6 flights]. Find:

[hint: numbers like 4.95E-5 should be written as .0000495]


a) P(first engine use does not malfunction) =


b) P(first flight has no engine malfunctions) =


c) P(no engine malfunctions in first week) =


d) P(at least one engine malfunction in first year) =

Answer 1

a) P(first engine use does not malfunction) = 1 - P(malfunction) = 1-0.0004 = 0.9996

b) P(first flight has no engine malfunctions) = (1 - P(malfunction))² = 0.9996² = 0.9992

c) P(no engine malfunctions in first week) = (P(first flight has no engine malfunctions))^6*7 = 0.9992⁴² = 0.966945

d) P(at least one engine malfunction in first year) = 1-(P(first flight has no engine malfunctions))^6*365 = 1-0.9992²¹⁹⁰ = 0.826695