Question

An aircraft uses three active and identical engines in parallel. All engines fail independently. At least one engine must function normally for the aircraft to fly successfully. The probability of success of an engine is 0.8. Calculate the probability of the aircraft crashing. Assume that one engine can only be in two states, i.e., operating normally or failed.

Answer 1

Solution:

In the given example, all the conditions for the binomial distribution are satisfied.

Here,

n = 3 No. of trials ,Here No.of engines

p = 0.8 Probability of success of an engine

Let X be the number of successes in the sample (i.e here number of successful engines in the sample)

X follows binomial(n = 3 , p = 0.8)

PMF of binomial is

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

Calculate the probability of the aircraft crashing.

Aircraft crashes iff all the engines failed. i.e if no one engine fly successfully.

P(Aircraft crashing) = P(X = 0)

=   (₃C ₀) * 0.8⁰ * (1 - 0.8)^3-0

= (3!/0!*3!) * 0.8⁰ * 0.2³

= 0.008

Answer is 0.008