Results 1 to 2 of 2

Math Help - Binomial Question or Counting Techniques?

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    2

    Binomial Question or Counting Techniques?

    Hi,

    I have a basic probability question that I just cannot understand..

    Three of twenty tyres in a store are defective. Four tyres are randomly selected for inspection. What is the probability that at least one defective tyre will be included?

    I can think of two solutions but don't understand why they are different / give different answers:

    1) There are 20C4 ways of choosing 4 tyres from 20. There are 17C4 ways of choosing 4 non-defective tyres.
    Hence P(at least 1 defective tyre) = 1 - P(four non-defective tyres)
    = 1 - 17C4 / 20C4
    = 0.5087..

    2) P(at least 1 defective tyre) = 1 - 4C0 * (3/20)^0*(17/20)^4
    =1-(17/20)^4
    =0.47799...

    My intuition tells me the first method is correct, using counting techniques. But how come the second method (binomial distribution) does not work? I know i have assumed that the rate of defect is 3/20, is this wrong?

    Thanks everyone
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Thanks
    1
    The second method is wrong, because the probability is not the same as you pick tyres.

    At first, the probability is 17/20, then 16/19, then 15/18, and last, 14/17.

    You cannot use a binomial distribution since the events are dependent.

    That said, the probability becomes the one in the first case.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Counting Techniques.
    Posted in the Statistics Forum
    Replies: 3
    Last Post: October 24th 2009, 03:14 PM
  2. Probability Probelms & Counting Techniques
    Posted in the Statistics Forum
    Replies: 1
    Last Post: June 10th 2008, 05:21 PM
  3. Probability Probelms & Counting Techniques
    Posted in the Statistics Forum
    Replies: 2
    Last Post: June 10th 2008, 04:58 PM
  4. Probability Probelms & Counting Techniques
    Posted in the Statistics Forum
    Replies: 2
    Last Post: June 10th 2008, 04:52 PM
  5. Data Help!!! Counting Techniques
    Posted in the Statistics Forum
    Replies: 2
    Last Post: March 3rd 2008, 03:33 PM

Search Tags


/mathhelpforum @mathhelpforum