Question

In the game of​ roulette, a player can place a ​$ 5 bet on the number 30 and have a 1/ 38 probability of winning. If the metal ball lands on 30​, the player gets to keep the ​$ 5 paid to play the game and the player is awarded an additional ​$ 175 . ​Otherwise, the player is awarded nothing and the casino takes the​ player's ​$ 5. Find the expected value​ E(x) to the player for one play of the game. If x is the gain to a player in a game of​ chance, then​ E(x) is usually negative. This value gives the average amount per game the player can expect to lose. The expected value is ​$ nothing . ​(Round to the nearest cent as​ needed.)

Answer 1

Let X : players net gain

If the metal ball lands on 30 , players net gain 175 + 5 = $180 with probability 1/38 and if metal ball lands other than 30 player looses $5 with probability 37/38

The expected value

E( X ) = X * P( X )

E( X ) = 180*(1/38) -5*(37/38)

E( X ) = - 0.13 or $(0.13)