For this discussion, select a game of chance, explain it briefly if it is likely to be unfamiliar to your classmates, then calculate probabilities of various outcomes like winning or losing in this game.

Game of Chance: Roulette

Roulette is a popular casino game that involves a spinning wheel with numbered slots and a ball. The objective of the game is to predict which slot the ball will land in after the wheel is spun. The slots on the wheel are numbered from 1 to 36, with half of them colored red and the other half colored black. In American roulette, there are also two additional green slots numbered 0 and 00.

To play roulette, the player places their bet on the table, indicating the number or group of numbers they want to bet on. There are many different types of bets in roulette, including betting on a single number, a group of numbers, the color of the slot (red or black), or whether the number will be even or odd. The payout for each type of bet varies depending on the odds of winning.

The probability of winning in roulette depends on the type of bet. For example, if a player bets on a single number in European roulette (without the 00 slot), the probability of winning is 1/37 or approximately 2.7%. If the player bets on red or black, the probability of winning is 18/37 or approximately 48.6%. The probability of winning a bet on an even or odd number is also 18/37 or approximately 48.6%.

In American roulette, the presence of the 00 slot increases the house edge and reduces the probability of winning for all types of bets. For example, the probability of winning a bet on a single number in American roulette is 1/38 or approximately 2.6%. The probability of winning a bet on red or black or even or odd is 18/38 or approximately 47.4%.