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Math Help - Easy prob question but I can't see it :(

  1. #1
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    Easy prob question but I can't see it :(

    A hunter has 2 hunting dogs.

    One day, on the trail of some animal, the hunter comes to a place where the road diverges into two paths. He knows that each dog, independent of the other, will choose the correct path with probability p. The hunter decides to let each dog choose a path, and if they agree, take that one, and if they disagree, to randomly pick a path. Is his strategy better than just letting one of the two dogs decide on a path?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Easy prob question but I can't see it :(

    Quote Originally Posted by perla View Post
    A hunter has 2 hunting dogs.

    One day, on the trail of some animal, the hunter comes to a place where the road diverges into two paths. He knows that each dog, independent of the other, will choose the correct path with probability p. The hunter decides to let each dog choose a path, and if they agree, take that one, and if they disagree, to randomly pick a path. Is his strategy better than just letting one of the two dogs decide on a path?
    Probability=p^2+2p(1-p)\times 0.5=p^2+p-p^2=p

    So, his strategy is exactly as good as just letting one of the two dogs decide on a path.
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    Thumbs up Re: Easy prob question but I can't see it :(

    interesting question. though i'm unable to conclude a way to answer your question, i have a feeling that this could be more than probability. it appeared as though it was a decision making problem... have listed the possibilities in the image below....
    Attached Thumbnails Attached Thumbnails Easy prob question but I can't see it :(-decision.jpg  
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    Re: Easy prob question but I can't see it :(

    Quote Originally Posted by alexmahone View Post
    Probability=p^2+2p(1-p)\times 0.5=p^2+p-p^2=p

    So, his strategy is exactly as good as just letting one of the two dogs decide on a path.
    Thank you for your reply. Why is there a 2 times p(1-p) and times 0.5?

    Regards
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    Grand Panjandrum
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    Re: Easy prob question but I can't see it :(

    Quote Originally Posted by perla View Post
    Thank you for your reply. Why is there a 2 times p(1-p) and times 0.5?

    Regards
    Because there are two ways of the dogs disagreeing on the path dog1 could be right and 2 wrong or dog1 could be wrong and 2 right.

    CB
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    Grand Panjandrum
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    Re: Easy prob question but I can't see it :(

    Quote Originally Posted by MAX09 View Post
    interesting question. though i'm unable to conclude a way to answer your question, i have a feeling that this could be more than probability. it appeared as though it was a decision making problem... have listed the possibilities in the image below....
    It is a pure probability problem, the decision rule is given the only question left is what is the probability of a correct outcome.

    Your third possibility is redundant it is already present as leaf nodes on the first two branches.

    CB
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    Re: Easy prob question but I can't see it :(

    i thought the problem was to decide which of the two methods was better. now i see it..
    the third offshoot from the centre was to analyse the second method by letting one of them pick a given way...
    As alexmahone posted it, both methods turned out to have the same outcome.

    A thought-provoking problem.
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