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 players are asked 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 0.8 and 0.2. the probabilities at c are .999 and .001. the probabilities at d are 0.5 and 0.5. finally, the probabilities at e are 0.95 and 0.05. draw the decision tree that represents this scenario. use proper symbols and label all branches clearly. calculate the expected value of this game.