Sum of Scores of 2 Dice

1. Sum of Scores of 2 Dice How would you represent the sum of scores on 2 dice? 123456 1 2 3 4 5 6 7 2 345678 3 456789 4 56789 10 5 6 789 10 11 6 789 10 11 12 How would you represent the sum of scores on 3 dice?

2. 123456 1 2 3 4 5 6 7 Take all the possible sums of 2 dice and then imagine you get a one on the next dice. 2 345678 3 456789 What would all the possible sums be for this scenario? 4 56789 10 5 6 789 10 11 6 789 10 11 12 3 4 5 6 7 8 456789 56789 10 6 789 10 11 789 10 11 12 89 10 11 12 13

3. 3 4 5 6 7 8 A reminder of the sum of three dice with the last number being one. 456789 56789 10 6 789 10 11 789 10 11 12 89 10 11 12 13 456789 Take all the possible sums of 2 dice and then imagine you get a two on the next dice. 56789 10 6 789 10 11 789 10 11 12 Do we have to do this another four times or can anyone see a quicker way by looking at these two examples? 89 10 11 12 13 9 10 11 12 13 14

4. What is the probability of scoring 10 when you roll 3 dice? (Decimal) What´s the probability of scoring 18 when you roll three dice? (Decimal) Why is the distribution symmetrical? Can you see any special number sequences in the table? Why does this sequence only exist up to a score of 8? 3 6 10 15 21 28 ??? 25 27 27 25 21 15 10 6 3 1

5. 3 4 5 7 8 6 45 7 8 9 6 5 7 8 9 10 6 45 7 8 9 6 5 7 8 9 10 6 7 8 9 10 11 6 5 7 8 9 10 6 7 8 9 10 11 6 7 8 9 10 11 12 8 9 10 11 12 13 6 78 9 10 11 7 8 9 10 11 12 9 10 11 12 13 14 8 9 10 11 12 13 7 8 9 10 11 12 9 10 11 12 13 14 10 11 12 13 14 15 8 9 10 11 12 13 First Layer Second Layer Third Layer 7 8 9 10 11 6 7 8 9 10 11 12 4 + 3 + 2 + 1 = 10 different ways to get a 6 8 9 10 11 12 13 9 10 11 12 13 14 10 11 12 13 14 15 Why doesn´t a score of 9 fit the sequence? 11 12 13 14 15 16 Third Layer

6. We just figured out that the score of 10 should occur just as frequently as a score of 11. Why hasn´t this happened?