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vipulgoyal
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For y < x, the point (x, y) must lie below the line y = x on the xy coordinate plane.
Hence, here the point (x, y) must be inside the triangle OMB.
Hence, required probability = (Area of OMB)/(Area of OAB)
Area of OAB = (base)*(height)/2 = 5*10/2
Area of OMB = (base)*(height)/2 = 5*(y-coordinate of M)/2
Hence, required probability = (y-coordinate of M)/10
Now, M is the intersection of line segment AB and x = y.
Equation of the line segment AB : x/5 + y/10 = 1
If y-coordinate of M is Y, then Y/5 + Y/10 = 1 ---> 3Y/10 = 1 ---> Y = 10/3
Hence, required probability = (10/3)/10 = 1/3
