Dice Problems — Revision Notes

⚡ 30-Second Revision

Views: adjacent is not opposite. Rolls: update all six positions in order. Probability: fairness and independence are assumptions. Two fair independent dice give 36 ordered outcomes; at least one six gives 11/36.

2-Minute Revision

Three visible faces are pairwise adjacent but do not usually determine all hidden labels. Four distinct neighbours identify an opposite. In the reference die, right then towards the observer gives top 5. For random throws, a sum of seven has six ordered routes, a sum of two one. Union counts subtract overlap; opposite-face labels do not control independence between throws.

5-Minute Revision

Track the reference die through a right roll and a forward roll, writing all six positions each time. Then list the six outcomes summing to seven and the eleven outcomes with at least one six. Explain why a single visible corner cannot establish the opposite of 1 without another condition.

Vyyuha Quick Recall

View, move, or throw? Choose geometry for the first two and a sample space for the third.