Results 1 to 9 of 9
Like Tree2Thanks
  • 1 Post By Plato
  • 1 Post By richard1234

Math Help - Statistics grocery store question

  1. #1
    Newbie
    Joined
    Jun 2012
    From
    Minnesota
    Posts
    20

    Statistics grocery store question

    Statistics Grocery Store Question
    I am a new online Math Help Forum Friend. I'm back to school after many years out and am taking Statistics. I have a problem that I cannot seem to solve. Can you help?

    A grocery produce manager inspects the corn supplied by a nearby farm. In a bushel of 30 ears of corn, the manager inspects 3 ears of corn. If 2 or more of the ears of corn are defective, the entire bushel is rejected. In this bushel, 5 ears of corn are defective. Find the number of ways that 2 or more ears of corn will be found defective by the produce manager.

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: Statistics grocery store question

    The bushel will be rejected in one of two ways:

    Case 1: Exactly two ears are defective.
    Case 2: Exactly three ears are defective.

    Case 1: We want the number of ways to choose three ears of corn such that two of them are defective (given that 5/30 are defective). Here, we are choosing two defective ears out of five, and one normal ear out of the remaining 25. This can occur in {{5}\choose{2}}{{25}\choose{1}} = 250 ways.

    Case 2: We want to pick all three defective ears out of the five. This can occur in {{5}\choose{3}} = 10 ways.

    The total number of ways that two or more defective ears is chosen is 250+10 = 260.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2012
    From
    Minnesota
    Posts
    20

    Re: Statistics grocery store question

    Thank you Richard. This was very difficult for me and after several hours of working on it, I went searching for help. I appreciate
    your writing out the explanation so that I can augment my learning.

    Now I have yet another question. I can see that there is a 5 over 2 in parentheses and a 25 over 1 in parenthesis and a 5 over the 3 in parentheses. How do those numbers get worked in order to equal the sums you found?

    Thank you.
    Last edited by u12480; June 17th 2012 at 07:51 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jun 2012
    From
    Minnesota
    Posts
    20

    Re: Statistics grocery store question

    I had one other question. Is there a name for the formula that you used to figure this out? Thank you.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1

    Re: Statistics grocery store question

    The numbers in the funny parentheses are "binomial coefficients".

    Binomial coefficient - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jun 2012
    From
    Minnesota
    Posts
    20

    Re: Statistics grocery store question

    So, if I haven't learned those yet is there another way to figure out this problem?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1597
    Awards
    1

    Re: Statistics grocery store question

    Quote Originally Posted by u12480 View Post
    So, if I haven't learned those yet is there another way to figure out this problem?
    If you have not had those yet, then you should not have been asked to do this question.
    Thanks from u12480
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: Statistics grocery store question

    Those are combinations, and they return binomial coefficients.

    Basically, the number of ways to choose k objects out of a set of n (order doesn't matter, this is called a "combination") is denoted {{n}\choose{k}} ("n choose k") and is given by

    {{n}\choose{k}} = \frac{n!}{(n-k)!k!}.

    For example, {{5}\choose{2}} = \frac{5!}{3!2!} = \frac{120}{6(2)} = 10
    Thanks from u12480
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Jun 2012
    From
    Minnesota
    Posts
    20

    Re: Statistics grocery store question

    I appreciate your replies. We are just starting to do binomial equations. Thank you for the explanation.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Statistics Grocery Store Question
    Posted in the New Users Forum
    Replies: 0
    Last Post: June 16th 2012, 08:03 PM
  2. Store
    Posted in the Algebra Forum
    Replies: 6
    Last Post: January 1st 2009, 12:27 PM
  3. 7-11 store
    Posted in the Algebra Forum
    Replies: 3
    Last Post: December 23rd 2008, 05:43 AM
  4. [SOLVED] Ideas on statistics equations for grocery prices
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 11th 2008, 09:25 PM
  5. Store Deduction
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: January 19th 2007, 12:46 PM

Search Tags


/mathhelpforum @mathhelpforum