Region R is defined as the region in the first quadrant satisfying the condition 3x 4y lt 12 Given t......

Region R is defined as the region in the first quadrant satisfying the condition 3x + 4y < 12. Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2?

Line 3x + 4y =12 cuts the x-axis at (4, 0) and y axis at (0, 3).
The region in the first quadrant satisfying the condition 3x + 4y < 12 forms a right triangle with sides 3, 4 and 5.
Area of this triangle = 6 sq.units.
The lines x = 2 and 3x + 4y = 12 intersect at (2, 1.5). So, the region r > 2, 3x + 4y < 12 also forms a right triangle.
This right triangle has base sides 2, 1.5. Area of this triangle = 1.5
Probability of the point lying in said region = 1.5/6 = 1/4

By: Amit Kumar