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Math Help - plane task

  1. #1
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    plane task

    Cannot find a solution for such task:

    There are a plane missing in one of two regions with probability 0.8 in the first and probability 0.2 in the second region. 10 helicopters have been sent to find the plane, each one of them can be sent to exactly one region. Each helicopter independently from other finds the plane with probability 0.2, if the plane is in concrete region.
    How many helicopters should be sent to each of regions in order to have probability to find the plane as big as possible? How big is this probability?

    This task is under Total probability formula/Bayes probability formula chapter, but I cannot figure out how to use them.
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  2. #2
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    Quote Originally Posted by waytogo View Post
    Cannot find a solution for such task:

    There are a plane missing in one of two regions with probability 0.8 in the first and probability 0.2 in the second region. 10 helicopters have been sent to find the plane, each one of them can be sent to exactly one region. Each helicopter independently from other finds the plane with probability 0.2, if the plane is in concrete region.
    How many helicopters should be sent to each of regions in order to have probability to find the plane as big as possible? How big is this probability?

    This task is under Total probability formula/Bayes probability formula chapter, but I cannot figure out how to use them.
    Maximise

    0.8Pr(X > 0) + 0.2Pr(Y>0)

    where X ~ Binomial(n, p = 0.2) and Y ~ Binomial(10-n, p = 0.2).

    Trial and error will be an efficient approach for finding the required value of n.
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