Results 1 to 4 of 4
Like Tree2Thanks
  • 1 Post By romsek
  • 1 Post By romsek

Thread: probability problem

  1. #1
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,681
    Thanks
    2389

    probability problem

    A line segment of length 5 is broken at two random points along its length. What is the probability that the shortest of the three new segments has length longer than 1?
    I'm going to assume that the distributions of the two points the segment is broken at are

    a) independent

    b) uniform[0,5]

    Plotting this we see the following boolean contour plot, showing as a function of the break points $x,y$

    whether the shortest segment has length less than 1.

    probability problem-clipboard01.jpg

    those tannish triangles are the where the criterion fails to be met.

    They have area $\dfrac{2\cdot 2}{2} = 2$ and there are two of them for a total area of $4$

    The area of the probability space is $5\cdot 5=25$

    so the probability that the criteria is met is

    $P[\text{shortest segment has length <1}]=1 - \dfrac{4}{25} = \dfrac{21}{25}$
    Thanks from Melody2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2013
    From
    Australia
    Posts
    261
    Thanks
    57

    Re: probability problem

    Thanks Romsek,
    This is a very interesting question and that boolean contour plot looks like a great tool but I do not understand it.
    Could you try and explain it to me.
    I'd really appreciate that.
    thanks
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,681
    Thanks
    2389

    Re: probability problem

    Quote Originally Posted by Melody2 View Post
    Thanks Romsek,
    This is a very interesting question and that boolean contour plot looks like a great tool but I do not understand it.
    Could you try and explain it to me.
    I'd really appreciate that.
    thanks
    that's just a plot of the area on the joint distribution where the criteria is met and where it's not.

    The tan triangles are where it's not.

    The purple area divided by the total area is the probability of meeting the criteria of the length of the smallest segment.

    We get away with such simple calculations because the joint distribution is uniform in both independent variables.

    This turns out to be $\dfrac {21}{25}$
    Thanks from Melody2
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Nov 2013
    From
    Australia
    Posts
    261
    Thanks
    57

    Re: probability problem

    Got it! Thanks )
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: Jan 21st 2011, 11:47 AM
  2. Probability Problem please help!
    Posted in the Statistics Forum
    Replies: 3
    Last Post: Apr 4th 2010, 07:38 PM
  3. Probability Problem please help!
    Posted in the Statistics Forum
    Replies: 5
    Last Post: Apr 1st 2010, 07:12 AM
  4. probability problem
    Posted in the Statistics Forum
    Replies: 2
    Last Post: Mar 30th 2010, 09:05 AM
  5. Replies: 0
    Last Post: Oct 8th 2009, 08:45 AM

/mathhelpforum @mathhelpforum