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# Line L passes through (5,0) and (0,10).If a point is

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Manager
Joined: 01 Nov 2007
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Line L passes through (5,0) and (0,10).If a point is [#permalink]  10 Mar 2008, 08:45
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Line L passes through (5,0) and (0,10).If a point is selelcted at random from the triangular region encircled by axis-x, axis-y, and line L, what is the probability that y<x?

Please kindly provide explanation.
Director
Joined: 10 Sep 2007
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Re: PS (probability) [#permalink]  10 Mar 2008, 09:01
I am not sure about exact answer.

Area of Whole traingle = 1/2*5*10 = 25
Area of triangle Between Y > 5 and Y <= 10 = 1/2*5*5 = 12.5
In second traingle all the values of Y will be greater than X so Prob. for Y > X = 12.5/25 = 1/2

However there will be case in which Y>X even within the lower triangle so I am not sure how to handle them.
E.g. (1,4) is valid point in lower triangle here Y>X so such probability also needs to be accounted for.

I can say that probability of X>Y will be around 1/4. So I will go by the answers rather than doing the whole calculations.
Intern
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Re: PS (probability) [#permalink]  10 Mar 2008, 15:58
2
KUDOS
As Abhijit said, the whole triangle is 25. The fraction of this larger triangle having points where y<x are contained in the smaller triangle whose sides are the x axis, the line having points (0,10) and (5,0), and the line y=x. The line y=x intersects the line with points (0,10)(5,0) at (10/3, 10/3):

y-10=(-10/5)(x-0) (Point slope form of line between 0,10 and 5,0)
y-10=(-2)(y) (sub y=x)
3y=10

The area of the smaller triangle is 1/2 * 5 * 10/3 = 25/3
The ratio of the smaller triangle to the larger is (25/3)/25 = 1/3
The probability is 1/3 that y<x
Senior Manager
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Re: PS (probability) [#permalink]  10 Mar 2008, 19:24
tritium6 wrote:
The fraction of this larger triangle having points where y<x are contained in the smaller triangle whose sides are the x axis, the line having points (0,10) and (5,0), and the line y=x. The line y=x intersects the line with points (0,10)(5,0) at (10/3, 10/3):

Awesome.... +1.

Like an idiot I drew a straight line parallel to x axis intersecting at 5 on the y-axis as the splitting point....
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Stay Hungry, Stay Foolish

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Re: PS (probability) [#permalink]  10 Mar 2008, 20:06
az780 wrote:
Line L passes through (5,0) and (0,10).If a point is selelcted at random from the triangular region encircled by axis-x, axis-y, and line L, what is the probability that y<x?

Please kindly provide explanation.

Imagine you create a full square here. We have 5*10=50 possible points.
Now the ways we can have y<x are (assuming integer values)

1,0 2,0 3,0 4,0 5,0

2,1 3,1 4,1 5,1

3,2 4,2 5,2

4,3 5,3

5,4

15 ways

15/50 = 3/10 aprox???
Re: PS (probability)   [#permalink] 10 Mar 2008, 20:06
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# Line L passes through (5,0) and (0,10).If a point is

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