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Math Help - finite probability question

  1. #1
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    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.
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  2. #2
    Grand Panjandrum
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    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 1, and that you choose a point x\sim U(0,1). Now the first part of the question becomes:

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

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

    CB
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  3. #3
    Grand Panjandrum
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    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 x<1/4 or x>3/4

    CB
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