Louisiana is busy designing new lottery “scratch-off” games. In the latest game, Bayou Boondoggle, the player is instructed to scratch off one spot: A, B, or C. A can reveal “Loser, ” “Win $1,” or “Win $50.” B can reveal “Loser” or “Take a Second Chance.” C can reveal “Loser” or “Win $500.” On the second chance, the player is instructed to scratch off D or E. D can reveal “Loser” or “Win $1.” E can reveal “Loser” or “Win $10.” The probabilities at A are .9, .09, and .01. The probabilities at B are .8 and .2. The probabilities at C are .999 and .001. The probabilities at D are .5 and .5. Finally, the probabilities at E are .95 and .05. Draw the decision tree that represents this scenario. Use proper symbols and label all branches clearly. Calculate the expected value of this game.
The expected value of scratch A =
The expected value of scratch B =
The expected value of scratch C =
The expected value of the game =