Results 1 to 6 of 6

Math Help - Probability Problem please help!

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    19

    Probability Problem please help!

    Please help! I'm not exactly sure where to start. I guess at first by figuring out all of the possible options and then is that it or what? But here's the problem: 6 red beads, 4 white beads, and 1 blue bead are placed in a line in random order. What is the probability that no two neighboring beads are the same color?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    Quote Originally Posted by sweeetcaroline View Post
    But here's the problem: 6 red beads, 4 white beads, and 1 blue bead are placed in a line in random order. What is the probability that no two neighboring beads are the same color?
    Well your sample space is S= 3!\times 6!\times4!\times1! Now you need to find the event space. If we have 11 positions, red can only be in one of the following ways:

    _ R _ R _ R _ R _ R _R

    R _ R _ R _ R _ R _R_

    So we only have 2! choices for red. Now no matter where we place white and blue they are not next to each other, so we have 5! ways of placing the remaining 5 beads.

    That is E= 2!\times5!

    P= \frac{E}{S} = \frac{2!\times5!}{3!\times 6!\times4!\times1!}
    Last edited by Anonymous1; March 31st 2010 at 06:11 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    19
    Thanks so much but why in the sample space is 3! included? Wouldn't it just be 6! x 4! x 1!?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    _ _ _ _ _ _
    We arranged the six red

    _ _ _ _
    Then the four white

    _
    Then the one blue.

    Now think of each one of these color blocks as its own entity. Then we have 3! ways of arranging the 3 entities.

    WAIT!

    S=11!
    Because we have 11! ways of arranging the 11 items.

    Sorry about that.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,689
    Thanks
    617
    Hello, sweeetcaroline!

    Edit: Plato is absolutely right . . . *blush*


    6 red beads, 4 white beads, and 1 blue bead are placed in a line in random order.
    What is the probability that no two neighboring beads are the same color?
    There are: . {11\choose6,4,1} \:=\:2310 possible orders.



    Place the 6 Red beads in a row, leaving a space between them.

    . . \begin{array}{ccccccccccccc} R & \_ & R & \_ & R & \_ & R & \_& R & \_ & R\end{array}


    Place the Blue bead is any of the 5 spaces: . 5 choices.


    Drop the 4 White beads in the remaining 4 spaces: . 1 way.


    Hence, there are: . 5\cdot1 \,=\,5 ways.


    Therefore, the probability is: . \frac{5}{2310} \;\;=\;\;\frac{1}{462}

    Last edited by Soroban; April 1st 2010 at 07:52 AM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by sweeetcaroline View Post
    the problem: 6 red beads, 4 white beads, and 1 blue bead are placed in a line in random order. What is the probability that no two neighboring beads are the same color?
    Can someone give me a line of these beads in which no two neighboring beads are the same color other than the five listed below?
    RWRWRWRWRBR
    RWRWRWRBRWR
    RWRWRWBWRWR
    RWRBRWRWRWR
    RBRWRWRWRWR
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: January 21st 2011, 11:47 AM
  2. job probability.....problem
    Posted in the Statistics Forum
    Replies: 1
    Last Post: July 14th 2010, 03:27 AM
  3. Replies: 0
    Last Post: October 8th 2009, 08:45 AM
  4. Probability Problem
    Posted in the Statistics Forum
    Replies: 4
    Last Post: March 13th 2009, 09:03 PM
  5. Probability problem
    Posted in the Statistics Forum
    Replies: 3
    Last Post: July 10th 2006, 06:33 AM

Search Tags


/mathhelpforum @mathhelpforum