# Probability of maximum of 2 uniform random variables

The random variables X and Y are independent, each with the uniform distribution on [−1, 1].

Find: $$P[max (X,Y) >0.5]$$ Apparently there is an easy approach without integration, but I am having trouble visualizing it. Thoughts?

-
possible duplicate of Expected value of max(x, y) –  kaine Nov 10 '13 at 20:34

Draw the square $[-1,1]\times[-1,1]$. Shade in the region where $X$ or $Y$ is greater than $0.5$. Calculate the proportion of the shaded area to the area of the square.