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?
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.