SOLUTION: The (simplified) probability of losing this bet is 47/54. If a player bets $18 on the $5 denomination, find the player's expectation. (Round your answer to two decimal places.)

Question 1199367: The (simplified) probability of losing this bet is 47/54.
If a player bets $18 on the $5 denomination, find the player's expectation. (Round your answer to two decimal places.)
Answer by proyaop(69) (Show Source): You can put this solution on YOUR website!
**1. Calculate the Probability of Winning:**
* Probability of winning = 1 - Probability of losing
* Probability of winning = 1 - (47/54) = 7/54
**2. Calculate the Expected Value**
* Expected Value = (Probability of Winning * Winnings) - (Probability of Losing * Bet Amount)
* Expected Value = (7/54 * $5) - (47/54 * $18)
* Expected Value = ($35/54) - ($846/54)
* Expected Value = -$811/54
* Expected Value ≈ -$15.02
**Therefore, the player's expected value of this bet is -$15.02.** This means, on average, the player can expect to lose $15.02 for each $18 bet.

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