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Dice Game Maths Investigation

Extracts from this document...

Introduction

Dice Game

          Introduction

              My aim in this investigation is to investigate three questions:

          1.     The probabilities of each of A, B or C winning the game.

          2.     Who will be the most likely winner?

          3.     The most likely length of the game in terms of the number of rolls

          of the dice to produce a winner.

          Predictions

              Before I actually do the game in the proper way I’m going to make

          a few predictions. This will help me to understand possible results

          better.

               I predict that C will be the most likely winner as it has the highest probability

          of winning the game when it’s his turn. I say this even though it takes its turn

          last. I believe B will be the second most likely winner as it too has the second

          highest probability; and the same goes for A- least likely for the same reason.

              As for the most likely length of game in terms of the number of rolls of the

          dice to produce a winner - I believe that the answer to this question could be 3

          as it is the first opportunity for C to win and it has a 50% chance of winning

          every throw it has (3/6).

...read more.

Middle

          Conclusion  

              Now that I’ve carried out the experiment and I’m happy that I did it in a clear

          and organised way I can come to a few conclusions. I believe at the present

          moment C has the highest probability in winning – (29/60) overall confirms this.

              Also another conclusion is that C was the most likely winner, I believe this

          was because on each throw it took, it had a 50% chance of winning whereas this

          wasn’t the case with A and B. A had only a 16.6% chance of winning and B

          had a reasonable 33.3% chance of winning each time it took a throw. I have a

          good idea that this was the telling factor in the results that I took down. I think

          that due to the percentage chance of winning C won the most and A the least.

              I am finding that trends are beginning to appear in the results. For a start from

          my results A never won on its first go. If B won it normally won on its first go as

          the next person to throw was C and it won frequently on the third throw – in fact

          it won thirteen out of fifteen times it won, on its first throw (the third throw).

...read more.

Conclusion

          amazing thirteen times out of that fifteen it won on its first throw (which was the

          game’s third throw). This was the main reason I decided that three rolls was the

          most likely.

              So, to sum up my answers are as follows:

          1.     P (Of A winning) = 3/13

                  (      B              ) = 5/13

                  (      C              ) = 5/13

          2.     B and C were the most likely winners equally.

          3. Three rolls                        

          Evaluation

              Overall my experiment has been a successful one and I’ve come to a few

          conclusions that seem to be getting towards firm conclusions, which I can rely

          on. I believe my experiment to be fairly reliable because I took the results down

          carefully and accurately. Also I collaborated my results with someone else to

          give me a more reliable look at my results and confirm any possible patterns.

          This made it increasingly reliable.

              However saying this I would have liked to done a bit more playing of the

          game as the more I played the game the more reliable the results would have

          been. Although one could argue playing the game over and over again may not

          help or influence any conclusions that one’s already drawn up. Also maybe I

          could have drawn a bigger probability tree to possibly help improve the reliability

          of my investigation and give me a clearer idea of a firmer conclusion.

...read more.

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