Results 1 to 3 of 3

Thread: finite probability question

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    22

    finite probability question

    A point X is chosen at random on a line sement AB. (a)show that the probability that the ratio of lengths AX/BX is smaller than a is = to a/(1+a). and (b) show that the probability that the ration of the length of the shorter segment to that of the longer is less than 1/3 is = to 1/2.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    5
    Quote Originally Posted by lauren2988 View Post
    A point X is chosen at random on a line sement AB. (a)show that the probability that the ratio of lengths AX/BX is smaller than a is = to a/(1+a). and (b) show that the probability that the ration of the length of the shorter segment to that of the longer is less than 1/3 is = to 1/2.
    You may as well assume that the line segment is of length $\displaystyle 1$, and that you choose a point $\displaystyle x\sim U(0,1)$. Now the first part of the question becomes:

    find $\displaystyle p(x/(1-x)<a)$ give $\displaystyle x\sim U(0,1)$.

    You do this by rearranging the condition $\displaystyle x/(1-x)<a$ into the form $\displaystyle x< ...$ where $\displaystyle ...$ is an expression in $\displaystyle a$ only.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    5
    Quote Originally Posted by lauren2988 View Post
    A point X is chosen at random on a line sement AB. (a)show that the probability that the ratio of lengths AX/BX is smaller than a is = to a/(1+a). and (b) show that the probability that the ration of the length of the shorter segment to that of the longer is less than 1/3 is = to 1/2.
    To do the second part we are being asked (same notation as before) to compute the probability that $\displaystyle x<1/4$ or $\displaystyle x>3/4$

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Distinct Bases for Finite Vector Spaces over Finite Fields
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 29th 2011, 12:31 PM
  2. Finite sum question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Mar 26th 2011, 05:04 AM
  3. Another finite question I need help with please
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Sep 11th 2009, 08:17 AM
  4. Please help me with this finite question
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Sep 11th 2009, 04:44 AM
  5. [SOLVED] Finite Math help? (probability)
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Feb 25th 2009, 02:54 PM

Search Tags


/mathhelpforum @mathhelpforum