Basic continuous random variable question: probability that x + y <= 0.5

[tanna89]

Randomly draw two numbers x and y from [0,1]. Find the probability that x + y <= 0.5


I request using integration as the tool. my hope is that I can extend this understanding to more complicated functions

 

[HallsofIvy]

Draw an xy- coordinate system. x, y in [0, 1] forms a square of area 1 (vertices at (0, 0), (1, 0), (1, 1), and (0, 1)). x+ y= 0.5 is the line from (0, 0.5) to (0.5, 0). $\displaystyle x+ y\le 0.5$ is that line and all points "below", "to the left" of that line. The portion that lies in the square is the triangle with vertices (0, 0), (0.5, 0), (0, 0.5). What is the area of that triangle?