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Probability
Level
3
Your friend invites you to play a game using 60 cards, numbered 1 to 60. If you pick a card that shows a multiple of 10, you gain $10. If you pick a card that shows a multiple of 4 (but not 10), you gain $4. Otherwise, you lose $5. What is the expected value of this game?
The answer is -1.7.
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1 solution
Let X be the value you would get (or lose). The first step is to calculate the probabilities: P(X=10)=6/60=1/10 P(X=4)=12/60=1/5 P(X=-5)=42/60=7/10
Thus, the expected value of the game is P(X=10) 10 + P(X=4) 4 - P(X=-5)*5 =1+4/5-7/2 =-17/10 = -1.7