A familiar probability question

  • Thread starter mesarmath
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hi,

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 ?
 
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  • #2
tiny-tim
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Hi mesarmath! :smile:
… but i could not figure out how the area above the curve x=yz represents that probability geometrically ?
(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.
 
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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.
thanks

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

thanks again :)
 

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