1.     XYZ company has designed a new
lottery scratch-off game. 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 0.9,
0.09, and 0.01 respectively. The probabilities at B are 0.8 and
0.2. The probabilities at C are 0.999 and 0.001. The probabilities
at D are 0.5 and 0.5. The probabilities at E are 0.95 and 0.05.
Calculate the expected value of the game.