Results 1 to 4 of 4

Math Help - Path Counting - Chances of two people meeting?

  1. #1
    ISK
    ISK is offline
    Newbie
    Joined
    Feb 2008
    Posts
    3

    Path Counting - Chances of two people meeting?

    I am having trouble with this problem.

    A network of city streets forms square bloacks as shown in the diagram below.
    ImageShack - Hosting :: librarypoolqs6.jpg

    Jeanine leaves the library and walks toward the pool at the same time as Miguel leaves the pools and walks toward the lbrary. Neither person follows a particular route, except that both are always moving toward their destination. What is the probability that they will meet if they both walk at the same rate?

    In addition, how would I solve this for a 1 by 1 grid, 2 by 2 grid, 3 by 3 grid,etc.?

    I know that you have to use Pascal's Triangle and the answer in the book is 35/128 but I don't know how to get this.
    Last edited by ISK; February 24th 2008 at 01:25 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,707
    Thanks
    1637
    Awards
    1
    Look carefully at the diagram you supplied.
    Did you mean to have a 4x4. You put a 4x3.
    This problem is usually done on a square grid.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    ISK
    ISK is offline
    Newbie
    Joined
    Feb 2008
    Posts
    3
    Yea sorry I messed it up, I fixed it.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,707
    Thanks
    1637
    Awards
    1
    Look at my diagram. If the two will meet that will happen at one of the points on the diagonal.
    Here are the number of paths from either the pool or the library to the diagonal \left( {\begin{array}{*{20}c}<br />
   A & B & C & D & E  \\<br />
   1 & 4 & 6 & 4 & 1  \\<br />
\end{array}} \right)
    You should recognize those numbers.
    The probability that they will meet at point C is  \left( {\frac{6}{{16}}} \right)\left( {\frac{6}{{16}}} \right).

    Now you calculate the probabilities of their meeting at each of the other points on the diagonal and add them up. If done correctly the answer will be \frac {35}{128}.

    Also, I have given you a pattern to follow for the other cases and a generalization.
    Attached Thumbnails Attached Thumbnails Path Counting - Chances of two people meeting?-libpool.gif  
    Last edited by Plato; February 24th 2008 at 03:00 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: February 14th 2011, 07:18 AM
  2. degree of a path, path homotopy.
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: March 19th 2009, 05:37 PM
  3. What are the chances?
    Posted in the Statistics Forum
    Replies: 3
    Last Post: June 28th 2008, 04:31 AM
  4. What are the chances?
    Posted in the Statistics Forum
    Replies: 2
    Last Post: May 5th 2008, 10:00 AM
  5. what are the chances?
    Posted in the Statistics Forum
    Replies: 6
    Last Post: January 14th 2006, 05:43 PM

Search Tags


/mathhelpforum @mathhelpforum