We define a bow-tie quadrilateral as a quadrilateral where two sides cross each other. An example of a bow-tie quadrilatera is shown below. distinct points are chosen on a circle. We draw all chords that connect two of these points. Four of these chords are selected at random. What is the probability that these four chosen chords form a bow-tie quadrilateral?

Question

We define a bow-tie quadrilateral as a quadrilateral where two sides cross each other.  An example of a bow-tie quadrilatera is shown below.  distinct points are chosen on a circle. We draw all  chords that connect two of these points. Four of these chords are selected at random. What is the probability that these four chosen chords form a bow-tie quadrilateral?

Bot · Answer

The probability that these four chosen chords form a bow-tie quadrilateral is 0.25, or 25%.