A jar contains 5 red, 4 green, and 3 blue marbles. In a game a player closes their eyes, reaches into the jar and randomly chooses two marbles.

The player wins $20 if both of their marbles are blue, $18 if both their marbles are green, and $16 if both their marbles are red. In all other cases the player loses the game. Suppose it costs $5 to play the game. Mathematically analyze this game and determine if it is in your financial interest to play the game.