Suppose we color the vertices of Cg9 red and blue, independently at random so that each vertex is red with probability 1/2 and blue with probability 1/2. For a fixed edge e, let A be the event that the vertices incident to e have different colors. What is Pr[A If the events A were independent for different edges e, with what probability would our coloring be proper? Are the events Ae independent? Why or why not