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    Application of the Binomial Distribution to an Aircraft

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    Suppose you are flying a four-engine aircraft on a 10-hour transoceanic flight. Assume that it has been established that the probability of an engine of the type you have on your aircraft failing during a 10-hour flight is 0.008. Determine the probability of all four engines failing during the flight.

    A student decided that this is a binomial distribution problem. Remember that the four characteristics of a binomial distribution are:

    Fixed number of trials
    Two possible outcomes
    Fixed probability of success
    Independence of events
    Evaluate the problem in terms of the four characteristics and explain whether you think it does or does not fit the characteristics of a binomial distribution. If not, which characteristics do not hold? Note that in determining whether or not a problem is â??binomialâ? or not, you must evaluate it against the four characteristics listed above.

    The student found that the probability of all four engines failing is 4.1E-09. Is that answer correct?

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    Solution Preview

    In general, for n independent trials with a probability p of success for each trial, the probability of m successes is P = nCm * p^m * q^(n-m), where q = 1-p is the probability of failure of a given trial and nCm = n!/(m!(n-m)!) is a binomial coefficient. In this case, we ...

    Solution Summary

    We use the binomial distribution to estimate the probability of failure of a four-engine aircraft on a transoceanic flight, given the probability of failure of any one of its engines.