Dice sum probability

Question

Simulate two separate dice (use random numbers with the appropriate range) being rolled 10 times. What are the percentage of rolls that resulted in a sum of 7, a sum of 2 and a sum of 11.

I came across this problem and have spent ages trying to figure out the algorithm for this...any help would be appreciated. I would show you what I came up with but i have nothing...

Answer 1

You need a random number generator that gives a uniform distribution on $[1,6]$ to be a die. Then loop from $1$ to $10$, rolling two dice each time. Total the dice and count the times you get $2, 7, 11$. Report the results

Answer 2

This looks like a programming exercise rather than a math exercise. Specifics will depend on your programming language, but it is going to be something like

n2 = n7 = n11 = 0;
for i = 1 to 10 do
  d1 = random(1,6) // get a random integer between 1 and 6
  d2 = random(1,6) // and another one
  s = d1 + d2
  if s == 2 then n2 = n2 + 1; fi
  if s == 7 then n7 = n7 + 1; fi
  if s == 11 then n11 = n11 + 1; fi
od
print "2's:  ", 10 * n2, "%"
print "7's:  ", 10 * n7, "%"
print "11's: ", 10 * n11, "%"

It's much more fun to try to figure out the expected number of 2's, 7's and 11's, but I'll leave that as (another) exercise.