4. When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over.
A. Why will some numbers come up more frequently than others?
B. Each die has six sides numbered from 1 to 6. How many possible ways can a number be rolled? In other words, we can roll (2,3) or (3,2) or (6,1) and so on. What are the total (x,y) outcomes that can occur?
C. How might you then estimate the percentage of the time a particular number will come up if the dice are rolled over and over?
D. Once these percentages have been calculated, how might the mean value of the all the numbers thrown be determined?
The solution is comprised of explanations to several problems regarding the frequency of dice rolls.