s: 1. For your selected die, state how many faces it has and determine how many outcomes are possible if your die is rolled two times. Ans: The die you have selected has 6 faces. If you roll the die two times, the total number of outcomes is 6*6 = 36. This is because, for each roll of the first die, there are 6 possible outcomes on the second roll, leading to 6*6 = 36 total outcomes. 2. Determine the number set that consists of all of the possible dice roll totals when two rolls are made. Ans: The number set that consists of all possible dice roll totals when two rolls are made is {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. This is because the smallest total you can get is 1+1=2 and the largest total you can get is 6+6=12. 3. Make a prediction for the total possible outcomes and the number set consisting of all possible dice roll totals if 3 rolls are made. Justify your answer with complete sentences. Ans: If 3 rolls are made, the total possible outcomes would be 6*6*6 = 216. This is because, for each of the 36 outcomes from the first two rolls, there are 6 possible outcomes on the third roll. The number set consisting of all possible dice roll totals would be {3, 4, 5, ..., 18}. This is because the smallest total you can get is 1+1+1=3 and the largest total you can get is 6+6+6=18. 4. Make a prediction for the total possible outcomes and the number set consisting of all possible dice roll totals if n rolls are made. You'll have to find the abstract relationship. Justify your answer with complete sentences. Ans: If n rolls are made, the total possible outcomes would be 6^n. This is because, for each outcome from the previous roll, there are 6 possible outcomes on the next roll. The number set consisting of all possible dice roll totals would be {n, n+1, n+2, ..., 6n}. This is because the smallest total you can get is rolling 1 n times and the largest total you can get is rolling 6 n times. 5. What if you rolled a die that had the same number of faces as your birth month when written as a number? What would be the total possible outcomes, and the number set consisting of all possible dice roll totals if n rolls are made? Justify your answer with complete sentences. Ans: If you rolled a die that had the same number of faces as your birth month (10), the total possible outcomes for n rolls would be 10^n. This is because, for each outcome from the previous roll, there are 10 possible outcomes on the next roll. The number set consisting of all possible dice roll totals would be {n, n+1, n+2, ..., 10n}. This is because the smallest total you can get is rolling 1 n times and the largest total you can get is rolling 10 n times. 6. Going back to your original die. Consider if there were infinite dice rolls. This would definitely produce an infinite number of possible outcomes. But, would it be a countably infinite set or an uncountable set? Justify your answer with complete sentences. Ans: If there were infinite dice rolls with a 6-sided die, it would produce a countably infinite set of outcomes. This is because the set of outcomes can be listed in a sequence