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Maths Statistics Coursework

Introduction: You are trying to make money by selling a game to friends. Each person pays a �1 for one throw of the dice. If they throw a 6 they win �10 – Investigate12345614576810From the table I can see that if I played the game for real I would be loosing more money than I was making. There would be a 1/6 chance of winning which means that for every �6 I made I would pay out �10.To make the game more profitable I am going to design another one using one dice. The game is “You throw the dice and if you get a 1 you win �5″Dice number123456No’ time thrown988997From the table above it shows that if the game was played for real it would make a small profit of �5 for every �50 that came in. There is still a 1/6 chance of winning but the prize money has been reduces so that for every 6 pounds that I took I would be paying out �5 so I would statistically be making a profit of �1 for every 6 throws that took placeFrom the previous results that I received I think that I should increase the amount of events that can take place. To do this I will need to have a extra throw or have another dice.To try to make a even bigger profit with this game I am going to make a totally different game with two dice. You throw the first one and you have to get a higher one to win, you pay �2 a go and win �5 if you role a higher numberWin15Loose75From this game you can see that you would make a profit testing the game showed that for every 100 goes you would make a profit of �75. To work out the probability for this you can draw a tree diagramThe probability for winning in that game is 15/36 this means that statically for every 36 players 15 of them would be winners. So for 36 plays you would take �72 of which �75 would be prize money. This shows that you should make a loss with the game but when it was tested a profit of �75 was. This happened because the game is based on luck it is not definite that 15 people in 36 would win.To make a better game I think that there should be a game with the same amount of events but with less possible winners. I have decided on a game, which you pay �1 and if the numbers are consecutive you win �5. The second consecutive number has to be higher e.g. 1,2 would be a win but 2,1 wouldn’tWin12Loose88In this game you take �100 which �65 is prize money. To find out a probability of there being consecutive numbers you can draw a grid, which shows what the probability of getting consecutive numbers with two throws of the dice.1,11,21,31,41,51,62,12,22,32,42,52,63,13,23,33,43,53,64,14,24,34,44,54,65,15,25,35,45,55,66,16,26,36,46,56,6From the above table it shows that the probability of getting a consecutive number is 5/36, which means every 36 players 5 of them, would be winners. With the players paying �1 you would make �36 and pay out �25.I found out that the last game I created the consecutive number would make the most money this happened when I was testing and statically it was correct. When testing it came out that I would make �35 out of every 100 games and statistically I would make �1 out of every 36 games.

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