Consider four square shaped ranches arranged in a 2x2 grid. One family lives on each ranch and each family builds a small house independently at a random spot within their property. The families then construct 4 straight line paths between the houses that go across property lines. The path forms a quadrilateral circuit path connecting all four houses which also serves as a boundary in which their children can play. What is the probability that their children can travel in a straight line between any two points without leaving the boundary? In other words, what is the probability that the boundary is a convex quadrilateral?
This is what I managed to do.
I am struggling to calculate the probability. How do I calculate the probability. Thank you in advance.
P=[0 0; 1 1; 1.5 0.5; 1.5 -0.5; 2 0];