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
    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, 04:14 PM
  2. Probability Probelms & Counting Techniques
    Posted in the Statistics Forum
    Replies: 1
    Last Post: June 10th 2008, 06:21 PM
  3. Probability Probelms & Counting Techniques
    Posted in the Statistics Forum
    Replies: 2
    Last Post: June 10th 2008, 05:58 PM
  4. Probability Probelms & Counting Techniques
    Posted in the Statistics Forum
    Replies: 2
    Last Post: June 10th 2008, 05:52 PM
  5. Data Help!!! Counting Techniques
    Posted in the Statistics Forum
    Replies: 2
    Last Post: March 3rd 2008, 04:33 PM

Search Tags


/mathhelpforum @mathhelpforum