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Find the probability of a defective item in a small sample

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data
    In a box there are 25 non defective details and 28 defective details find propability from two random extraction that
    c) One of them is non-defective


    2. Relevant equations



    3. The attempt at a solution
    I think I know the answer but I need explanation.
     
  2. jcsd
  3. Sep 19, 2010 #2
    Re: Propability

    If you think you know the answer, how about sharing your solution with us?
     
  4. Sep 19, 2010 #3
    Re: Propability

    permutation


    C25(1) * C28(1)/ C53(2) = 700/(2756/2) =1400/2756

    But still need explenation though.
     
  5. Sep 19, 2010 #4
    Re: Propability

    You have the right idea but you need to check your numbers.

    There are C(53,2) ways to draw 2 items from the box. We assume all of these are equally likely. Of these, how many consist of one defective and one non-defective?
     
  6. Sep 19, 2010 #5
    Re: Propability

    It should be about 50% chance of one consisting non defective and the other being defective I THINK

    in practice assume we have 50 balls 25 good and 25 bad ,we draw 2 balls and it should be G1/2 * B1/2 ?
     
  7. Sep 19, 2010 #6
    Re: Propability

    Close but not quite right. The complication is that the draws are not independent events. Since you are drawing balls without replacement, if you draw a good ball on the first draw it changes the probability that you will draw a bad draw on the second draw. Numerically, there won't be much difference, in this case, though-- you could say the draws are "almost independent".

    One way to approach this type of problems is the way I outlined previously. All C(50,2) combinations of 50 balls taken two at a time are equally likely. So count the number of ways to draw one good and one bad, then divide by C(50,2).
     
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