Given a random experiment of casting two balance dice. 1. Find the sample space S. 2. Let m = max(a, b + 2) and n= max(a +2, b). Find m and n. 3. If A denotes the event of casting a total of m, write A as a subset of S. 4. Find the probability of casting a total of m. 5. Interpret your answer to the preceding question in terms of a relative frequency. 6. Find the probability of casting a total of at most n.