• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Maths Dice Investigation

Extracts from this document...

Introduction

Rules

 10 counters are placed in the centre of the dodecahedron. Two dice are then rolled the amount of the two numbers on the dice are then recorded. A counter from the centre of the dodecahedron is then placed into “A” wins or “B” wins depending on the sum of the two numbers.

E.g.

3 + 2 = 5 therefore it goes into A wins

6 + 4 = 10 so obviously B wins

And so on. this continues until there are no counters remaining inside the dodecahedron.

Prediction

I predict that B will win because it is more likely to get the numbers that when added together make the sum of the numbers found in B.

Results

Game

Counters in A

Counters in B

Who won ?

1

5

5

draw

2

4

6

b won

3

3

7

b won

4

5

5

draw

5

5

5

draw

6

4

6

b won

7

3

7

b won

8

6

4

a won

9

2

8

b won

10

4

6

b

The results table

...read more.

Middle

3

4

5

6

1

2

3

4

5

6

7

2

3

4

5

6

7

8

3

4

5

6

7

8

9

4

5

6

7

8

9

10

5

6

7

8

9

10

11

6

7

8

9

10

11

12

image00.png

P(A Wins) = 12/36 = 1/3

P(A Wins) = 24/36 = 2/3

The possibilities found above are from using my possibility diagram.

All of the green coloured squares have a higher probability of being obtained, as shown in the diagram above. Therefore the game is unfair. For example, there are 5 different ways of getting 8 whereas there are only 2 ways of reaching 11.

The probability of A winning is 1/3 and B winning 2/3. Showing that the game is foul not fair.                                       Extension Work

The probability of A winning is 1/3, but this only applies to one counter. I am now going to find out the probability of A winning a game instead of winning a counter.

...read more.

Conclusion

Pascal’s triangle

I have formed this triangle by arranging the results from the first 5 rows which have been taken from the various A and B. From this I could see a pattern developing. The pattern that I developed was the two numbers diagonally above the number were added together to get the bottom number.

E.G.

This triangle is called Pascal’s triangle.

Overall conclusion

From my findings it becomes evident to me that both the probability of B winning one counter and the game is considerably more likely than it is for A to win a counter and the match. The  probability of B winning a counter is 2/3 and the likely hood of B winning the game is 0.855. These statistics confirm to me that the game is foul because there is not an equal opportunity of a draw or A or B winning.

...read more.

This student written piece of work is one of many that can be found in our GCSE Beyond Pythagoras section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Beyond Pythagoras essays

  1. Beyond Pythagoras

    a�+b�=c� is the theorem ? (2n+1) �+ (2n (n+1)) � = (2n (n+1) +1) � (2x1.5+1) �+(2*1.5(1.5+1)) �=(2x1.5(1.5+1)+1) � 4�+7.5�=8.5� 16+56.25=72.25 Therefore 72.25=72.25 which is correct, which therefore means my formula so far works for the length of the shortest side.

  2. Beyond Pythagoras

    Tn = a + ( n - 1 ) d + 1/2 ( n - 1 ) ( n - 2 ) c 4 + ( n - 1 ) 8 + 1/2 ( n - 1 ) ( n - 2 )

  1. Beyond Pythagoras

    is + 2 this is because this is the only way all the smallest sides of a triple in the sequence would be even. Small I will use the method I used before for working out the nth term of something which always has the same amount of difference between each sequence: (2n)

  2. Was Maths invented or discovered?

    A much simpler way to show that maths was discovered is by understanding that a scientific explanation shows that maths was evident for the first time during the occurring of the Big Bang that led to the development of the universe and all its planets.

  1. Research on Pythagoras and his work.

    the mental act of generalisation, to appreciate the originality of this Pythagorean contribution. In fact today we have become so mathematically sophisticated that we fail even to recognise 2 as an abstract quantity. There is a remarkable step from 2 ships + 2 ships = 4 ships, to the abstract

  2. Beyond Pythagoras.

    Just in case I will test this formula in the next term: 2n+1 Nth term Length of shortest side 2 5 2x2=4 4+1=5 (correct) I now have to work out the formula for the middle side. I predict that the formula has got to do with something about the differences in lengths.

  1. The Die Investigation.

    Player \ nth term Attempt 1 Attempt 2 Attempt 3 Attempt 4 A (simplest form) 1/6 5/108 25/1944 125/34992 A (LCD) 3/18 15/324 75/5832 375/104976 B (simplest form) 5/18 25/324 125/5832 625/104976 C (simplest form) 5/18 25/324 125/5832 625/104976 I then noticed some patterns emerging, such as: P(B winning)

  2. Investigate the probability of someone rolling a die and the probability of it landing ...

    x 1 = 25 6 3 2 6 3 2 648 Here I found that there was a pattern and this was that each time there is another round the difference increases by 5. I will now test my theory to see if it is correct.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work