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Nines and Tens

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Both 9 and 10 can be made up in 2 different ways by adding pairs of the numbers 1, 2, ... 6, that is

9 = 3 + 6 = 4 + 5

10 = 4 + 6 = 5 + 5

Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?