Question

In the game of​ roulette, a player can place a ​$ 4 bet on the number 27 and have a StartFraction 1 Over 38 EndFraction 1 38 probability of winning. If the metal ball lands on 27​, the player gets to keep the ​$ 4 paid to play the game and the player is awarded an additional ​$ 140 . ​ Otherwise, the player is awarded nothing and the casino takes the​ player's ​$ 4 . What is the expected value of the game to the​ player? If you played the game 1000​ times, how much would you expect to​ lose?

Please work problem step by step please thank you

Answer 1

Solution:-

Given that

In the game of​ roulette, a player can place a ​$ 4 bet on the number 27 and have a StartFraction 1 Over 38 EndFraction 1 38 probability of winning. If the metal ball lands on 27​, the player gets to keep the ​$ 4 paid to play the game and the player is awarded an additional ​$ 140 . ​ Otherwise, the player is awarded nothing and the casino takes the​ player's ​$ 4

What is the expected value of the game to the​ player? If you played the game 1000​ times, how much would you expect to​ lose?

The probability of wining,

The probability of losing =

a)

The expected value of the game to the player is,

  

  

= -0.21053 (for one game)

b)

The expected value of lose for 1000 games is,

= 1000 * expected value of lose for one game

= 1000 * -0.21053

= -210.53

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