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Math Help - Out of every 100 jobs

  1. #1
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    Out of every 100 jobs

    Question : Out of every 100 jobs received at a computing center, 50 are of class1, 30 of class 2 and 20 from class 3

    i) A sample of 30 jobs is taken without replacement. Find the probability that the sample will contain 10 jobs of each class.

    ii) A sample of 3 jobs is taken with replacement, find the probability that there will be exactly 12 jobs of class 2
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    Hello, zorro!

    Out of every 100 jobs received at a computing center:
    50 are of class 1, 30 of class 2 and 20 of class 3.

    i) A sample of 30 jobs is taken without replacement.
    Find the probability that the sample will contain 10 jobs of each class.

    Answer: . \frac{{50\choose10}{30\choose10}{20\choose10}}{{10  0\choose30}}



    ii) A sample of 30 jobs is taken with replacement.
    Find the probability that there will be exactly 12 jobs of class 2

    Answer: . {30\choose12}(0.3)^{12}(0.7)^8

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    Thanks Soroban

    Quote Originally Posted by Soroban View Post
    Hello, zorro!


    Answer: . \frac{{50\choose10}{30\choose10}{20\choose10}}{{10  0\choose30}}




    Answer: . {30\choose12}(0.3)^{12}(0.7)^8


    how did u get (0.3)^{12}(0.7)^8
    Last edited by zorro; December 17th 2009 at 06:50 PM. Reason: Still some issue with the solution
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  4. #4
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    Quote Originally Posted by zorro View Post
    how did u get (0.3)^{12}(0.7)^8
    It follows a binomial distribution. Tick the boxes for each criterion:

    1. Only two possible outcomes: Class 2 (success) and not class 2 (failure).

    2. 30 independent trials: n = 30.

    3. Probability of success in each trial stays the same: p = 30/100 (because it's sampling with replacement).
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    I confusion

    Quote Originally Posted by mr fantastic View Post
    It follows a binomial distribution. Tick the boxes for each criterion:

    1. Only two possible outcomes: Class 2 (success) and not class 2 (failure).

    2. 30 independent trials: n = 30.

    3. Probability of success in each trial stays the same: p = 30/100 (because it's sampling with replacement).

    I also though it was binomial but i couldnt understand how he got (0.7)^8 could u please explain me from where did he get 8 from n-x = 30 - 12 = 18
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  6. #6
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    Quote Originally Posted by zorro View Post
    I also though it was binomial but i couldnt understand how he got (0.7)^8 could u please explain me from where did he get 8 from n-x = 30 - 12 = 18
    You're correct. Soroban made a typo. (Note: There is also a typo in your original question which Soroban fixed in his quote ....).
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    Thanks for justifying

    Quote Originally Posted by mr fantastic View Post
    You're correct. Soroban made a typo. (Note: There is also a typo in your original question which Soroban fixed in his quote ....).

    thanks Mr fantastic and Soroban for helping me with the question
    cheers guys
    Last edited by mr fantastic; December 18th 2009 at 09:26 PM. Reason: Too many beers.
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