An aircraft uses three active and identical engines in parallel. All engines fail independently. At least...

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.

Expert Solution

here we use binomial distribution with parameter n=3 and p=0.8 as condition independent and equal probability of binomial distribution satisfied.

and for Binomial distribution ,P(X=r)=ⁿC_rp^r(1-p)^n-r

required probability of the aircraft crashing=P(X=0)=0.008 ( using ms-excel =BINOMDIST(0,3,0.8,0))

required answer is 0.008

orchestra answered 2 years ago

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