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 re(3): Not faster, simpler, or better by ed bottemiller)

There are the same number of points inside a triangle as on the triangle's perimeter, but there still is a zero probability of a random point in the square being on the perimeter of the triangle.

Think of the one-to-one correspondence of the set of integers with the set of integers that are divisible by 1,000,000. There are the same number: aleph-null. But if you take an integer at random, it's not likely to be divisible by 1,000,000. In the aleph-1 case of lines vs areas, it's even more drastic.

Posted by Charlie on 2008-03-18 17:01:00