- #1
danmanchester
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Hi all, I've got a past paper question that goes something like this:
An aeroplane has four engines. During a certain journey, each engine fails with a probability of 0.1, independantly of the others. The aeroplane can fly when at least two engines are working. Calculate:
A) The probability that the aeroplane will complete the journey.
B) The probability that the aeroplane will complete four journeys with no engine failures. State clearly any assumptions you make.
Ok so I've decided this is a binomial distribution problem; for part A) I have assigned X to be the r.v. "number of engines failing" where X~B(4,0.1).
I'm looking for Pr(X ≤ 2) = 1 - (Pr(X = 3) + Pr(X = 4))
= 1 - (4C3X0.1^3X0.9 + 4C4X0.1^4)
= 1 - 3.7 x 10^-3
= 0.9963 (which as far as answers go, seems relatively plausible?).
As for part B), I have absolutely no ideas! If someone would be so kind as to assist it'd be much appreciated :)
Cheers,
Dan
An aeroplane has four engines. During a certain journey, each engine fails with a probability of 0.1, independantly of the others. The aeroplane can fly when at least two engines are working. Calculate:
A) The probability that the aeroplane will complete the journey.
B) The probability that the aeroplane will complete four journeys with no engine failures. State clearly any assumptions you make.
Ok so I've decided this is a binomial distribution problem; for part A) I have assigned X to be the r.v. "number of engines failing" where X~B(4,0.1).
I'm looking for Pr(X ≤ 2) = 1 - (Pr(X = 3) + Pr(X = 4))
= 1 - (4C3X0.1^3X0.9 + 4C4X0.1^4)
= 1 - 3.7 x 10^-3
= 0.9963 (which as far as answers go, seems relatively plausible?).
As for part B), I have absolutely no ideas! If someone would be so kind as to assist it'd be much appreciated :)
Cheers,
Dan