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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?

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.

Re: PS (probability) [#permalink]
10 Mar 2008, 15:58

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This post received 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

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.... _________________

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???

gmatclubot

Re: PS (probability)
[#permalink]
10 Mar 2008, 20:06