An aircraft has four major subsystems that determine its safety: mechanical, ele

Question

An aircraft has four major subsystems that determine its safety: mechanical, electrical, hydraulics, and communications. The aircraft will crash if two or more systems fail at the same time. Assume that each system fails independently with a component probability of failure during a flight of p=103. The probability that the aircraft will crash during a flight is a×106, where a is a constant. What is the closest integer value to a? (For example, if the probability of crash is 3.02×106 or 2.92×106, the answer would be 3.) Please give me a step by step solution.

Explanation / Answer

P( fail)=10-3=0.001 thus probability of no fot fail P(no fail)=1-0.001=0.999

P(2 or more failing)=P(2 fail)+P(3 fail)+P(4 fail)= 1-(P(0 fail)+P(1 fail))

=1-[ (0.999)^4+4C1*(0.001)*(0.999)^3]

=5.99^-06

thus answer is 6

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