Three points are chosen at random inside a square. Each point is chosen by choosing a random x-coordinate and a random y-coordinate.

A triangle is drawn with the three random points as the vertices. What is the probability that the center of the square is inside the triangle?

(In reply to

Faster, simpler, better by FrankM)

I see that most of those who tried complex solutions arrived at 1:4 as the probability. I arrived at this with my "guess" (meaning I didn't create any proof) that since the maximum area of an enclosed triangle was half of the square, then the average area of all triangles would be one quarter (for any triangle). Does that work? If so, does it work just for the center of the square? (No interesting way to computerize this, that I could see, so I'll settle for that guess.)