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 six-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(6, 0.003)

Where n = 6, p = 0.003

Binomial probability distribution is

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

a)

p( x = 1) = 6C1 0.0031 0.9975

= 0.01773

b)

p( x = 2) = 6C2 0.0032 0.9974

= 0.000133

c)

p( X >2) = 1 - (p(x = 0) + p( x = 1) + p(x = 2) )

= 1 - (0.9976 + 0.01773 + 0.00013)

= 0.000005539

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