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A familiar probability question

  1. Apr 4, 2010 #1

    i have been studying for GRE subject

    and i saw this question but i could not solve it

    x , y and z are selected independently and at random from the interval [0,1], then the probability that x is bigger than y*z is ?

    the answer is 3/4

    but i want to know how? , i guess it should be solved by double integral.

    thanks in advance for any help

    edit: i just figured out that [itex] \int_{0}^{1} \int_{0}^{1} (1-yz) dy dz = 3/4 [/itex]
    but i could not figure out how the area above the curve x=yz represents that probability geometrically ?
    Last edited: Apr 4, 2010
  2. jcsd
  3. Apr 4, 2010 #2


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    Hi mesarmath! :smile:
    (it ain't a curve, it's a surface :wink:)

    Because for each value y and z, the proportion of x > yz is the proportion below the surface, which is yz/1, and the proportion of x > yz is the proportion above the surface, which is (1 - yz)/1.
  4. Apr 4, 2010 #3

    so we were looking for a volume,
    curve was the thing that makes me confused

    thanks again :)
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