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Math Help - Probability question

  1. #1
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    Probability question

    Hello, could you help me

    Probability of failure of each airplane engine is equal to p.
    Airplane engines break down independently of each other.
    Airplane can fly, if work at least half of the existing engines.
    For which values ​​of p is a twin-engined plane safer than four-engined plane?

    How to get the inequality?

    Thank you
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  2. #2
    MHF Contributor

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    Re: Probability question

    If an airplane has two engines then "at least half of the engines working" is 1 or 2 engines working. The probability of exactly one engine breaking down is 2p(1- p) and the probability of neither breaking down is (1- p)^2 so the probability or "at least half of the engines working" is 2p(1- p)+ (1- p)^2= 2p- 2p^2+ 1- 2p+ p^2= 1- 2p- p^2.

    If an airplane has four engines, then "at least half of the engines working" is 2 or three or four engines working. The probability of exactly two engines breaking down is (4!/(2!)(2!)p^2(1- p)^2= 12p^2(1- p)^2. The probability of exactly one engine breaking down (so three working) is 3p(1- p)^3. The probability of no engine breaking down (so all four working) is (1- p)^4. Add those to find the probability of "at least half of the engines working".
    Thanks from feferon11
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