I'm working on assigning a probability to this problem:
The choice of a point from the interior of a square with opposite vertices $(-1, 1)$ and $(1,1)$ where the event C occurs if the sum of the coordinates of the point is less than $\frac{1}{2}$.
I think this would be: $\int^{1}_{-1}Pr(X=x) * (\int^{\frac{1}{2} - x}_{-1}Pr((Y = y)|(X = x))$ $dy)$ $dx$
Does this look roughly right? If so, how would I go about assigning a numerical value to this integral?
Thank you!