SOLUTION: A plane has three engines—a central engine and an engine on each wing. The plane will crash only if the central engine fails and at least one of the two wing engines fails. The

Algebra ->  Statistics  -> Normal-probability -> SOLUTION: A plane has three engines—a central engine and an engine on each wing. The plane will crash only if the central engine fails and at least one of the two wing engines fails. The      Log On


   

Question 1142617: A plane has three engines—a central engine and an engine on each wing. The plane will crash only if
the central engine fails and at least one of the two wing engines fails. The probability of failure
during any given flight is 0.005 for the central engine and 0.008 for each of the wing engines.
Assuming that the three engines operate independently, what is the probability that the plane will
crash during a flight?
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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The plane will crash if and only if one of the following events will happen


    - (a)  central and left engines fail

    - (b)  central and right engines fail

    - (c)  central and both left and right engines fail.



The probabilities for each of these events are


       P(a) = 0.005*0.008*(1-0.008) = 0.00003968

       P(b) = 0.005*0.008*(1-0.008) = 0.00003968

       P(c) = 0.005*0.008*0.008     = 0.00000032


The probability of the crash is the sum P = P(a) + P(b) + P(c) = 0.00007968 (approximately).    ANSWER