Find the Probability That Ten Dice Sum to a Multiple of Seven

Ten dice are rolled, and a win occurs when their total is divisible by seven. How would you compute the probability of winning? ### Constraints and Clarifications The report specifies ten dice and the divisibility rule but does not specify faces, fairness, or dependence. For this practice calculation, assume independent fair six-sided dice with outcomes 1 through 6. State how the calculation would change if those assumptions were different. No reward amount is supplied, so the task is to calculate the win probability rather than a monetary expected value. ### What a Strong Answer Covers Count totals or residues without treating possible sums as equally likely. Provide an exact expression for the probability and explain why it is or is not exactly one seventh. ### Follow-up Questions - How would you handle biased dice with known face probabilities? - How can a seven-state recurrence avoid tracking every possible total?