1. Team DD

2. The player pays $25 to play. He/she will roll 2 dice. If he/she rolls a sum of 2, then he/she will win $175. If he/she rolls a sum of 3, then he/she will win $125. If he/she rolls a sum of 8, then he/she will win $50. If the player rolls anything besides those three sums, he/she loses the game and wins nothing. 3. Theoretical X 2 = ((150+6.25)^2*(1/36))+((100+6.25)^2*(2/36)) +((25+6.25)^2*(5/36))+((25+6.25)^2*(28/36))=1714.41Expected value=X= (150*(1/36))+(100*(2/36))+(25*(5/36))+(25*(28/36))= $-6.25 On average, players can expect to lose $6.25. So in the long run, the casino makes an average of $6.25 every time someone plays.X (money made)P(x)$1501/36$1002/36$255/36$-2528/36X= 1714.41= 41.41On average, the money the player wins or loses varies by $41.41. 4. Simulation VideoTo simulate this game, we will be using the randINT function on our calculator to generate 50 random numbers between 1 and 6. These 50 numbers will represent what we get when we roll the first die 50 times. Next, we will generate another set of 50 random numbers between 1 and 6 which will represent what we get when we roll the second die 50 times. Then we will find the sum of the first roll and the second roll for each of the 50 trials to find out how much money we would win. This will help us figure out the expected value and the standard deviation of our simulation data. 5. Simulation Expected value=X= (150*(2/50))+(100*(2/50))+(25*(7/50))+(-25*(39/50))X= $-6.00 X 2 = ((150+6)^2*(2/50))+((100+6)^2*(2/50))+((25+6)^2*(7/50))+ ((-25+6)^2*(39/50))=2363 X= 2363= 48.61 X (money made)P(x)$150 $1002/50$257/50$-25Data (RandINT)2/5039/50 6. ReflectionThis game could be a success if put into a casino because it is attractive to the player while still having a house advantage, as the simulation data and the theoretical values prove. There is a house advantage of approximately 12% for both (6.25/50=0.125 and 6.00/50=0.12). The theoretical probability shows a slightly larger loss for the player (which is the expected value) but a smaller standard deviation. A smaller standard deviation means that the money players lose varies less for the theoretical data than the simulation data. This game could be improved upon by having a smaller house advantage. We would do this by changing the amount of money players pay compared to what they win.