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Math Help - cant find my mistake anywhere

  1. #1
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    cant find my mistake anywhere

    each of the 3 identical boxes has 2 drawers. the first box, one a gold watch in each drawer. the 2nd box, has a silver watch in each drawer and the 3rd box has a gold watch in one drawer and a silver in the other. what is the probability of finding a gold watch in one drawer of a box given that the other drawer has a silver watch?

    my working:

    P ( gold l silver) = P ( gold and silver ) / P (silver)
    = (1/3) / ( 1/3 + 1/6)
    = 2/3

    but the answer was 1/3

    may i know what went wrong?
    should i use bayes rule to solve this, how do i go about doing it?

    thanks!
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  2. #2
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    It's because P(gold & silver) is really P(gold in the SECOND draw you open & silver in the FIRST draw you open)

    So not only did you have to pick that box, you had to pick the drawers in the correct order. So P(gold & silver) is actually 1/3 x 1/2 = 1/6, not 1/3
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  3. #3
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    hmm the answer in my text says it is 1/3 but i got 2/3.

    i dont really get what you are trying to say
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  4. #4
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    I'm saying you just need to be more specific/careful when writing down what you're trying to find the probability of

    You are looking for *P(gold in the second draw you open | silver in the first draw you open)

    You're right to use Bayes rule

    So * = P(gold in the second draw you open and silver in the first draw you open)/P(silver in the first draw you open)

    Now the only way to get silver in the first AND gold in the second here is to not only choose the correct box (with the gold and silver), but to open the silver draw first. These are independent events so you multiply the probabilities. The probability of picking the right box is 1/3, and the probability of picking the silver draw first is 1/2

    So, P(gold second & silver first) is 1/3 x 1/2 = 1/6

    Then P(silver first) = 3/6 = 1/2 (3 silver draws from a total of six)


    So, P(gold 2nd|silver 1st) = (1/6)/(1/2) = 1/3
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  5. #5
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    oh! i get what you mean now! thanks thanks!!!
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  6. #6
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    No problem

    Another related & fun "what's wrong with this argument" question is why is the answer not 1/2? You've got yourself a silver draw, so now you know you're either dealing with the all silver box or the gold/silver box, so it should be equal probabilities that the next drawer is gold or silver, right?

    (No, but why?)
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  7. #7
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    isit becos you need to first pick the box before you can open it to know that the first draw is a silver hence need to consider 3 boxes instead of 2?

    whoa this is stimulating(:
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