Results 1 to 8 of 8

Math Help - negative binomial

  1. #1
    Junior Member
    Joined
    Jun 2008
    Posts
    53

    negative binomial

    The probability that a machine produces a defective item is 0.01. Each item is check as it's produced. Assume these are independent trials and compute the probability that at least 100 items must be checked to find 1 defective item.

    answer: 0.3967

    ---
    I let x= 100, r= 1,

    so

    99C0 * (0.01)(0.99)^99, which gives 0.003967

    Wrong answer. Explain please.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member bleesdan's Avatar
    Joined
    Jun 2008
    Posts
    37
    I think what you found is the wrong probability.
    What you are looking for is the probability that, after 99 items have gone by, you still haven't found a defective one. Then, anything that comes after it is irrelevant, because the first time you find a defective one, you will have checked at least 100 items.

    So, you want to find the probability that you get 99 undefective items.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2008
    Posts
    53
    Well, if I dont multiply by the 0.01 I get the right answer.
    But that's not what the question asks, or it doesn't seem so to me.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member bleesdan's Avatar
    Joined
    Jun 2008
    Posts
    37
    Why are you multiplying by .01?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jun 2008
    Posts
    53
    It's the formula for a negative binomial.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jun 2008
    Posts
    53
    Formula for a negative binomial:

    x-1 C r-1) (p^r)(1-p)^x-r
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by amor_vincit_omnia View Post
    The probability that a machine produces a defective item is 0.01. Each item is check as it's produced. Assume these are independent trials and compute the probability that at least 100 items must be checked to find 1 defective item.

    answer: 0.3967

    ---
    I let x= 100, r= 1,

    so

    99C0 * (0.01)(0.99)^99, which gives 0.003967

    Wrong answer. Explain please.
    The probability that at least 100 must be checked is the probability that the first 99 are not defective, which is 0.99^{99} \approx 0.3697

    RonL
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by amor_vincit_omnia View Post
    The probability that a machine produces a defective item is 0.01. Each item is check as it's produced. Assume these are independent trials and compute the probability that at least 100 items must be checked to find 1 defective item.

    answer: 0.3967

    ---
    I let x= 100, r= 1,

    so

    99C0 * (0.01)(0.99)^99, which gives 0.003967

    Wrong answer. Explain please.
    You have calculated the probability of exactly 100 items checked before the first defective, rather than at least 100 items ........ There's a big difference.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: July 15th 2010, 06:33 AM
  2. Why isn't this example a negative binomial
    Posted in the Statistics Forum
    Replies: 3
    Last Post: July 11th 2010, 02:06 AM
  3. Negative Binomial
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: July 20th 2009, 06:14 PM
  4. Replies: 1
    Last Post: March 12th 2009, 12:09 AM
  5. Relation between Negative Binomial and Binomial Distros
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 5th 2007, 07:59 AM

Search Tags


/mathhelpforum @mathhelpforum