*Was asked this question in an interview, so not sure what the optimal answer is, but here goes:*

Given a rectangle with length ***l*** and breadth ***b***, I pick 4 random points inside it. What is the probability that the 4 points lie on the same half of the rectangle?

Notes:

 1. Two halves of the rectangle are defined by a single line passing through the intersection of its diagonals. So the rectangle cannot be divided into two halves of any arbitrary shapes of equal length.
 2. A line passing through a picked point and the center does not contain another picked point. That is, A line passing through any two picked points does not pass through the center of the rectangle (Intersection of the diagonals).

Addition: (Maybe a Hint)

I was asked about 3 points first. They saw my approach and were satisfied and then asked me what if there were 4 points.

***Answer***

>! 9/16

The one to prove it gets the check mark.