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 $\frac{4}{36}\ast 100=11.11\mathrm{\%}$.

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 $\frac{5}{36}\ast 100=13.89\mathrm{\%}$.

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.