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Probability Problem Using Formula for Combinations

  1. Mar 16, 2010 #1
    1. The problem statement, all variables and given/known data Each of 12 refrigerators of a certain type has been returned to a distributor because of the presence of a high pitched oscillating noise. Suppose that 5 of these 12 have defective compressors and the other 7 have less serious problems. If they are examined in random order, let X = the number among the first 6 examined that have a defective compressor. Compute the following:

    P(x = 1)

    E(X)

    E(X^2)

    2. Relevant equations



    3. The attempt at a solution I'm getting really hung up here. I know my sample size is 6 refrigerators. 5 of the twelve are defective. My chances of picking a defective unit on the first try is 5/12.

    Someone told me that it was [(5 choose 3)(7 choose 3)]/(12 choose 6). I just don't understand how to do this well enough, so I don't know if it is the right answer or not. And I want to know how to do it anyway.
     
  2. jcsd
  3. Mar 16, 2010 #2

    Dick

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    Don't double post the same question. Ok? So what is [(5 choose 3)(7 choose 3)]/(12 choose 6) supposed be the answer to? Can you delete any other posts you have on this question and just concentrate on one?
     
  4. Mar 16, 2010 #3
    To get one bad compressor in a sample of 6, you have to choose 1 from the group of 5 that have bad compressors and 5 from the group of 7 that don't. Then to get the probability you divide by the number of ways to choose 6 from the 12 sample total. How do you express that in combinations language?

    My apologies. I didn't even realize I had posted my question once before. I put your answer to that one here. So I'll go and delete that one. I'm sorry about that. One of those days.
     
  5. Mar 16, 2010 #4
    I'm working the hint you gave me in my first (forgotten) post. While I work through it, I would like to delete my old post, but can't figure out how to do it. I can edit it, but I can't figure out how to delete it.
     
  6. Mar 16, 2010 #5
    Okay, so I set up the problem as [(5 choose 1)(7 choose 5)]/(12 choose 6) which yields appx 0.1136.

    Now I have to find E(X) for this. I know that E(X) = The Summation of [x*p(x)]. I don't know what x, or p(x) is though. Am I supposed to be using the probability that I found from this prior question?
     
    Last edited: Mar 16, 2010
  7. Mar 17, 2010 #6

    Dick

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    So far you've just found p(1). How many more do you need to find to compute E(X)? What's the range of possibilities of the number of bad compressors in a sample of 6?
     
  8. Mar 17, 2010 #7
    So would I need to find p(2) through p(6) [p(6) would be zero, so it is really just through p(5)].

    Then once I do this. I need to multiply x(subscript i) * p(x(subscript i).

    If I'm following this correctly, then I will have (1*.1136) + [2*p(x2)] + ...+ [6*p(x6)].

    Am I on the right track here?
     
  9. Mar 17, 2010 #8

    Dick

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    Sure, just like your Poisson problem, it's not that hard once you know what the parts are. Don't forget there is a p(0) too (which doesn't contribute to E(X)).
     
  10. Mar 17, 2010 #9
    Beautiful! So after I have done this step, then I find E(X^2) by doing the exact same thing, except that the value of X is squared right?

    I wish you were my teacher instead of this other guy.
     
  11. Mar 17, 2010 #10

    Dick

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    Yes, that's what you do.
     
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