XYZ company has designed a new lottery scratch-off game. The player is instructe
ID: 3331542 • Letter: X
Question
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.
Explanation / Answer
Solution:
Expected value of the game = (0*0.9)+(1*0.09)+(50*0.01)+(0*0.8)+0.2[(0*0.5)+(1*0.5)+(0*0.95)+(10*0.05)]+(0*0.999)+(500*0.001) = 1.29
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