The probability that an airplane engine will fail in a transcontinental flight i

Question

The probability that an airplane engine will fail in a transcontinental flight is 0.003. Assuming that engine failures are independent of each other, what is the probability that on a certain transcontinental flight, a five-engine plane will experience:

(a) Exactly one engine failure? (Round your answer to five decimal places.)


(b) Exactly two engine failures? (Round your answer to six decimal places.)


(c) More than two engine failures? (Note: In this event, the airplane will crash. Round your answer to nine decimal places.)

Explanation / Answer

X ~ Binomial (n,p)

Where n = 5 , p = 0.003

Binomial probability distribution is

P(X) = nCx px ( 1 - p)n-x

a)

P(1) = 5C1 0.0031 0.9974

= 0.01482

b)

P(2) = 5C2 0.0032 0.9973

= 0.000089

c)

P( X > 2) = P( X >= 3)

= P( X = 3) + P( X = 4) + P( X = 5)

= 5C3 0.0033 0.9972 +5C4 0.0034 0.9971 +5C5 0.0035 0.9970

= 0.000000269

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