Analysis: Four vertices are randomly selected from the six vertices of a regular hexagon. There is a selection method of C64= 15, and the possibility of each case is the same, so it is a classical probability. By enumerating, we can calculate the number of methods whose quadrangles are rectangles, and then we can calculate the proportion.

Solution: Four vertices are randomly selected from six vertices of a regular hexagon, and there are C64= 15 selection methods.

The method that their quadrangles as vertices are rectangular is three, which is known from classical probability.

The probability that their quadrilateral as the vertex is a rectangle is equal to 3 15 = 1 5 C(64) is the permutation and combination number, which means that 4 is randomly selected from 6, and the algorithm is 6! / [4! (6-4)! ]= 15

The condition of enclosing a rectangle is that the two sides are parallel, so the probability of only 3 in a * * * is 1/5.