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In the game of​ roulette, a player can place a ​$9 bet on the number 24 and have a StartFraction 1 Over 38 EndFraction probability of winning. If the metal ball lands on 24​, the player gets to keep the ​$9 paid to play the game and the player is awarded an additional ​$315. ​ Otherwise, the player is awarded nothing and the casino takes the​ player's ​$9. What is the expected value of the game to the​ player

Respuesta :

Answer:

- $0.47

Here, negative sign depicts the expected loss

Explanation:

Data provided in the question:

Bet amount for number 24 = $9

Probability of winning on number 24 = [tex]\frac{1}{38}[/tex]

Award amount for number 24 = $315

Probability of losing on number 24 = 1 - [tex]\frac{1}{38}[/tex] = [tex]\frac{37}{38}[/tex]

Losing amount = $9

Now,

The expected value of the game to the player

= Winning amount × Probability of winning - Losing amount × Probability of losing

= ( $315 × [tex]\frac{1}{38}[/tex] ) - ( $9 × [tex]\frac{37}{38}[/tex] )

= 8.29 - 8.76

= - $0.47

Here, negative sign depicts the expected loss

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