Take the square $[0,1]^2$ we take $n$ random lines through the square. You can choose random lines by choosing a point on one of the sides of the squares and randomly choosing a different point on any of the other three sides and then drawing a line connecting them.
What is the probability that after $n$ of these random lines the largest region is greater than or equal to $0.5$?
Any tips or cases help, thanks.