Question

In the casino game of American roulette, the wheel is divided into 38 compartments numbered 1 through 36, 0, and 00. One-half of the numbers 1 through 36 are red, the other half black, and 0 and 00 are green. Of the many types of bets that may be placed, one type involves betting on the outcome of the color of the winning number. For example, one may place a certain sum of money on red. If the winning number is red, one wins an amount equal to the bet placed and the amount of the bet is returned; otherwise, one loses the amount of the bet. If a player placed a $57 bet on red and a $57 bet on black in a single play in American roulette, what would be the expected value of his winnings? (Round your answer to the nearest cent.)

Answer 1

E(x) = 57(18/38) - 57(20/38) = 27 - 30 = -3

Therefore, expected value is a loss of $3.