Results 1 to 6 of 6

Math Help - Cereal boxes

  1. #1
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Cereal boxes

    A cereal manufacturer is evaluating a new design for the box of its leading brand. Ten people are shown the new and old box design. Each is asked which one he or she likes best. If each person doesn't have a preference and simply selects one of the two designs at random, what is the probability of each of all 10 selecting the new design?

    The answer is 1/1024.

    Why is the total number of combination possibilities 2^{10}\text{?}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1
    The are two choices and ten people.
    The number of functions from a set of ten to a set of two is 2^{10}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2010
    Posts
    40
    Quote Originally Posted by dwsmith View Post
    A cereal manufacturer is evaluating a new design for the box of its leading brand. Ten people are shown the new and old box design. Each is asked which one he or she likes best. If each person doesn't have a preference and simply selects one of the two designs at random, what is the probability of each of all 10 selecting the new design?

    The answer is 1/1024.

    Why is the total number of combination possibilities 2^{10}\text{?}
    Because each person has 2 choices. For each of the 2 choices person 1 has, person 2 has 2 choices.
    So if we work only with 2 persons, the number of choices will be 2 * 2 = 2^2
    If we extend the same reasoning to 3 persons, the number of choices will be 2*2*2
    = 2^3

    etc.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Now, how can I figure out the probability that 9, 8, 7, and 6 people select the new design?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1
    Quote Originally Posted by dwsmith View Post
    Now, how can I figure out the probability that 9, 8, 7, and 6 people select the new design?
    This is the number  \sum\limits_{k = 6}^9 {\dbinom{10}{k}} . WHY?

    I should that is the number of 6,7,8, or 9 prefer the new design.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by Plato View Post
    This is the number  \sum\limits_{k = 6}^9 {\dbinom{10}{k}} . WHY?
    Because 10 choose 6 + 7 + ... + 9 is the total.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 12
    Last Post: January 16th 2011, 06:22 AM
  2. Replies: 3
    Last Post: December 8th 2010, 08:55 AM
  3. The judge, and 12 boxes
    Posted in the Math Puzzles Forum
    Replies: 7
    Last Post: December 25th 2009, 10:05 PM
  4. A balls and boxes problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 1st 2008, 12:46 PM
  5. Boxes of Candy
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: January 14th 2007, 06:30 AM

/mathhelpforum @mathhelpforum