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# Region R is defined as the region in the first quadrant satisfying the

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Region R is defined as the region in the first quadrant satisfying the [#permalink]
Given 3x + 4y < 12

In Slope Intercept Form: y < -(3/4)x + 3

The Region represented by this inequality is all the Area UNDERNEATH the downward sloping line BUT ONLY in quadrant 1.

This region described above underneath the Line 3x + 4y = 12 ends up forming a Right Triangle with:

Y Axis from (0 , 0) up to (0 , 3) as One Leg

and

X Axis from (0 , 0) up to (4 , 0) as Second Leg

The Region in which the X-Coordinate of Point P (r) is > 2 is defined by the Region to the RIGHT of the Vertical Line X = 2 but INSIDE the Right Triangle.

Since this Vertical Line divides the Whole Right Triangle into 2 Similar Triangles:

Probability = (Area of Smaller Right Triangle) / (Area of ENTIRE Right Triangle)

Corresponding Side of Smaller Triangle / Corresponding Side of ENTIRE Triangle = 2/4 = 1/2

Therefore, because the triangles are Similar Triangles:

(Area of Smaller Triangle) / ( Area of ENTIRE Triangle) = (1)^2 / (2)^2 = 1 /4

Probability = 1/4

-C-

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Re: Region R is defined as the region in the first quadrant satisfying the [#permalink]
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Re: Region R is defined as the region in the first quadrant satisfying the [#permalink]
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