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With two dice the following totals are possible

....... Dice A .. Dice B

  1. 2 - 1 ..... 1
  2. 3 - 1 ..... 2
  3. 3 - 2 ..... 1
  4. 4 - 1 ..... 3
  5. 4 - 2 ..... 2
  6. 4 - 3 ..... 1
  7. 5 - 1 ..... 4
  8. 5 - 2 ..... 3
  9. 5 - 3 ..... 2
  10. 5 - 4 ..... 1
  11. 6 - 1 ..... 5
  12. 6 - 2 ..... 4
  13. 6 - 3 ..... 3
  14. 6 - 4 ..... 2
  15. 6 - 5 ..... 1
  16. 7 - 1 ......6
  17. 7 - 2 ..... 5
  18. 7 - 3 ..... 4
  19. 7 - 4 ..... 3
  20. 7 - 5 ..... 2
  21. 7 - 6 ..... 1
  22. 8 - 2 ......6
  23. 8 - 3 ..... 5
  24. 8 - 4 ..... 4
  25. 8 - 5 ..... 3
  26. 8 - 6 ..... 2
  27. 9 - 3 ..... 6
  28. 9 - 4 ..... 5
  29. 9 - 5 ..... 4
  30. 9 - 6 ..... 3
  31. 10 - 4 ..... 6
  32. 10 - 5 ..... 5
  33. 10 - 6 ..... 4
  34. 11 - 5 ..... 6
  35. 11 - 6 ..... 5
  36. 12 - 6 ..... 6

So, there are 36 different combinations of how the dice might land and 6 of those total 7. Therefore it is 6 chances in 36 that you'll get 7, which reduced to 1 in 6.

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Q: What is the probability of getting sum 7 if you throw two dice?
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