As part of a game, players choose from red, blue, and green tiles and place some of each into two bags, A and B. They must choose a unique number of tiles for each color in each bag, using at least 1 and no more than 9 tiles of each color. Then another player draws one tile from each bag. Points are earned for drawing 2 tiles of the same color.

a. One player places 1 red, 5 green and 3 blue tiles in Bag A, and 6 red, 4 green, and 2 blue in Bag B. What is the probability that the second player draws 2 tiles of the same color?

b. Drawing two tiles of the same color, one from each bag, earns points worth 3 times the total number of tiles for that color in both bags. For example, if there is a total of 6 red tiles in the bags and 2 red tiles are drawn, a player earns 18 points. What is the expected point value of drawing two tiles of the same color, one from each bag, assuming the same combinations of tiles described in part a?

c. Explain how the expected value you calculated in part b compares to the overall probability of earning points. What does the expected value mean within the context of this situation?