Computing Pr(f(x) != g(x))
I am not sure how others compute Pr(f(x) != g(x)).
It isn't so hard to do analytically, but there are a lot of cases to consider, depending on which boundary of the square the lines cross.
I now have one that just does the cases where both lines intersect the top and bottom of the square. By symmetry, the cases that intersect the left and right sides should be the same.
That leaves out the ones where lines intersect top or bottom and side. Those might have smaller area (probability) but maybe not too much smaller.
So far, it is close enough to one of the answers that I will go for that one. The other cases are enough harder to write that I won't try them.
