1. By: Sarah Aristizábal Ramos May 29th 2013 7.3

2. (2) Yellow Ball: $0 (1) Green Ball: $2 (1) Blue Ball: $5 (1) Purple Ball: $10 (1) Pink Ball: $20

3. Set Up: 1. Get the cardboard and put it in front so that people can’t see what is being done. 2. Get the boxes and open them. 3. Put one ball into each box and then close them. 4. Put the cardboard away, and the game is ready to play. 5. Wait until a costumer comes.

4. Playing the Game: 6. The costumer will pay $8.50. 7. The costumer picks one of the six boxes. 8. The costumer will open the box and see the ball’s color. 9. The costumer will then receive the amount of money that the ball in the box chosen represents. 10. The game is over. 11. Before the next turn a cardboard will be put in front of the boxes as before. 12. The owner will open all the boxes and change the marbles of box randomly. 13. The boxes will be closed and the cardboard will be put away. 14. The next customer pays to play and the game starts again.

5. Yellow Ball: 2/6 or 1/3 = 33.33% Green Ball: 1/6 = 16.67% Blue Ball: 1/6 = 16.67% Purple Ball: 1/6 = 16.67% Pink Ball: 1/6 =16.67% Costumer Getting Something: 4/6 or 2/3 = 66.67% Costumer Making Profit: 2/6 or 1/3 = 33.33% Owner Making Profit: 4/6 or 2/3 = 66.67%

6. Yellow Ball: 15 times Green Ball: 14 times Blue Ball: 7 times Purple Ball: 7 times Pink Ball: 7 times

7. Yellow Ball: 15/50 or 3/10 = 30% Green Ball: 14/50 or 7/25 = 28% Blue Ball: 7/50 = 14% Purple Ball: 7/50 = 14% Pink Ball: 7/50 = 14% Costumer Getting Something: 35/50 or 7/10 = 70% Costumer Making Profit: 14/50 or 7/25 = 28% Owner Making Profit: 36/50 or 18/25 = 72%

8. Yellow Ball: 2/6 × 0 = 0 = $0.00 Green Ball: 1/6 × 2 = 2/6 = $0.33 Blue Ball: 1/6 × 5 = 5/6 = $0.83 Purple Ball: 1/6 × 10 = 10/6 = $1.67 Pink Ball: 1/6 × 20 = 20/6 = $3.33 Total: $6.16 Cost to Play: $8.50

9. $8.50 × 100 = $850.00 $6.16 × 100 = $616.00 $850 - $616 = $234.00 After playing 100 times the school should expect to receive $850.00 and pay out $616.00. In total the school profit would be $234.00.

10. Yellow Ball: 15/50 × 0 = 0/50 = $0.00 Blue Ball: 14/50 × 2 = 28/50 = $0.56 Green Ball: 7/50 × 5 = 35/50 = $0.70 Purple Ball: 7/50 × 10 = 70/50 = $1.40 Pink Ball: 7/50 × 20 = 140/50 = $2.80 Total: $5.46

11. $8.50 × 50 = $425.00 $5.46 × 50 = $273.00 $425.00 - $273.00 = $152.00 If the school played and got this results he should expect to receive $425.00 and pay out $273.00. The profit would be $152.00.

12. Experimental: $152.00 × 2 = $304.00 Theoretical: $234.00 If the trial had continued to 100 trials and the results had been the same the school would have earned $304.00 which is much more than what should be earned based in theoretical probability ($234.00). This happened because the results weren’t how the theoretical probability said they could be. When playing the game the results can always change because theoretical probability is what people should get based on statistics. In a real game people can get lucky and earn more than thought. They can also have bad luck and loose more money than thought.

13. I think my game should be chosen because there is a 2/3 chance of getting a box with a ball worth something. For someone who doesn’t know how to analyze a probability game this game seems fair. To those who know how to analyze probability games this game can seem fair because there isn’t a huge difference between the expected value and the price to play. In some games these two prices have a huge difference between them. I also think it should be chosen because it makes profit for the school. People will want to play this game because you can win up to $20.00, it seems fair, and is really fun.