Three bags contain different numbers of blue and red marbles. A bag is selected using a die which has three A faces, two B faces, and one C face. One marble is then randomly selected from the bag. Determine the probability that the marble is:
Three purple vases labeled A, B, and C containing blue and red marbles. Vase A has 2 blue and 3 red marbles. Vase B has 1 blue and 4 red marbles. Vase C has 3 blue and 2 red marbles.