A flea moves around the vertices of a triangle in the following manner: Whenever it is at vertex i it moves to its clockwise neighbor vertex with probability pi and to the counterclockwise neighbor with probability qi = 1 − pi, i =

1, 2, 3.

(a) Find the proportion of time that the flea is at each of the vertices.

(b) How often does the flea make a counterclockwise move that is then followed by five consecutive clockwise moves?