For this project, you will analyze the famous casino game,Roulette. In the game of Roulette, there is a wheel consisting of38 numbers: 18 black numbers, 18 red numbers, and 2 green numbers(0 and 00). The wheel is spun and a ball is released into thewheel. As the wheel comes to a stop, the ball will land on one ofthe numbers. A player will place their bet before the wheel isspun. A player can make the following bets (along with otherbets):

Single (or multiple) number

1^st, 2^nd or 3^rd column (e.g. 1,4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34)

1^st, 2^nd or 3^rd dozen (e.g. 1through 12)

Odd / Even (does not include 0 or 00)

Red / Black

1 through 18 or 19 through 36

Please answer the following questions based on the game ofRoulette:

What is the probability of betting on all odds and winning?

What is the probability of betting on the 2^nd dozenand winning?

A player bets on the number 5 in the first game; then bets onnumber 22 in the second game. Did the player’s odds of winningchange from the first to the second game? Explain.

What is a better bet: all reds or all evens? Explain. (Hint: 0and 00 are not included in an all even bet)

If a player always bets on 00, what is the expected winnings (orloses) when playing 20 games of Roulette given the player receives$100 if they win and owes $1 if they lose?

If a player always bets on 3 and 23, what is the expectedwinnings (or loses) when playing 75 games of Roulette given theplayer receives $120 if they win (on either number) and owes $3 ifthey lose?

If a player always bets on the 2^nd dozen (13 to 24),what is the expected winnings (or loses) when playing 25 games ofRoulette given the player receives $32 if they win and owes $15 ifthey lose?

If you are playing Roulette, how would you bet? Would you play alot of games or try to win a lot on one or two games?