Answer:
37.5%
Step-by-step explanation:
If you draw this rectangle you will see that it has a width of 4 (from (0,0) to (4,0)) and a height of 3 (from (0,0) to (0,3)). Now lets draw a line from (0,0) to (3,3) this is the group of points inside the rectangle where x=y. Notice that this line divide the initial rectangle in two figures, a triangle and a quadrilateral:
triangle:
with vertices in (0,0), (0,3) and (3,3)
quadrilateral:
with vertices in (0,0), (3,3), (4,0) and (4,3)
For each point of the triangle it is true that:
[tex] y \geq x [/tex]
And for each point in the quadrilateral it is true that:
[tex] x \geq y [/tex]
triangle area = [text] \frac{3*3}{2} = 4.5 [/text]
rectangle area = [text] 3 + \frac{3*3}{2} = 7.5 [/text]
Therefore:
[tex] P(y>x) = \frac{4.5}{12} = 0.375 = 37.5% [/tex]
