Roll two dice virtually (by calculator: [APP] 10. Prob Sim, or by your phone or other device) \( 36,50,100,1000 \), and 10,000 times. How many times is the sum \( 5 ? \) How many times is the sum \( 6 ? \) Find these as percentages. How many ways (out of 36) can the dice sum to 5? Order matters. List the ways here. What is this as a percentage? How many ways (out of 36) can the dice sum to \( 6 ? \) Order matters. List the ways here. What is this as a percentage? Why does this happen?

Step 1 ：Roll the two dice virtually for \( n \) times, where \( n = 36, 50, 100, 1000, 10000 \). Record the number of times the sum is \( 5 \) and \( 6 \).

Step 2 ：Compute the percentages of the obtained sums by dividing the number of occurrences by \( n \) and multiplying by 100.

Step 3 ：There are \( 4 \) ways to sum to \( 5 \) with order matters: \( (1,4),(2,3),(3,2),(4,1) \). The percentage is \(\frac{4}{36} * 100 = 11.11\% \).

Step 4 ：There are \( 5 \) ways to sum to \( 6 \) with order matters: \( (1,5),(2,4),(3,3),(4,2),(5,1) \). The percentage is \(\frac{5}{36} * 100 = 13.89\% \).

Step 5 ：The probability of summing to a particular number depends on the number of ways the two dice can produce that sum out of the total possible outcomes of 36.