Answer:
EV = $-0.125
For one game, the outcome cannot be predicted, even though you are more likely to lose money.
For 100 games, you are expected to lose about $12.50
Explanation:
Expected value is the sum of the product of all possible outcomes by their payouts. In this case, there are only 2 possible outcomes. You either win by tossing 3 three heads with three coins or lose.
The probability of winning (P(w)) is:
[tex]P(w)=0.5*0.5*0.5\\P(h)=0.125[/tex]
Therefore, the probability of losing (P(l)) is:
[tex]P(l)=1-0.125\\P(l)=0.875[/tex]
The expected value (EV) for the game is:
[tex]EV= 6*0.125 - (1*0.875)\\EV = -0.125\\[/tex]
For one game, the outcome cannot be predicted, even though you are more likely to lose money than win. As for 100 games, since the expected value is negative, you are expected to lose money (about $12.50).
