Louisiana is busy designing new lottery scratch-off games. In the latest game, Bayou Boondoggle, the player is instructed to scratch off on 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.
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