Refer to the Problem 3-33 for details about the game of roulette. Another bet in a roulette game is called a “straight up” bet, which means that the player is bet-ting that the winning number will be the number that she chose. In a game with 0 and 00, there are a total of 38 possible outcomes (the numbers 1 to 36 plus 0 and 00), and each of these has the same chance of occurring. The payout on this type of bet is 35 to 1, which means the player is paid 35 and gets to keep the original bet. If a player bets $ 10 on the number 7 (or any single number), what is the expected monetary value (expected win)?
In Problem 3-33 The game of roulette is popular in many casinos around the world. In Las Vegas, a typical roulette wheel has the numbers 1–36 in slots on the wheel. Half of these slots are red, and the other half are black. In the United States, the roulette wheel typically also has the numbers 0 (zero) and 00 (double zero), and both of these are on the wheel in green slots. Thus, there are 38 slots on the wheel. The dealer spins the wheel and sends a small ball in the opposite direction of the spinning wheel. As the wheel slows, the ball falls into one of the slots, and that is the winning number and color. One of the bets available is simply red or black, for which the odds are 1 to 1. If the player bets on either red or black, and that happens to be the winning color, the player wins the amount of her bet. For example, if the player bets $ 5 on red and wins, she is paid $ 5 and she still has her original bet. On the other hand, if the winning color is black or green when the player bets red, the player loses the entire bet.