Question

If you toss two dice 1,000 times, how many times do you expect to have the sum of the two dice equal to four?


about 250


about 167


about 83


about 42

Answer 1

Each die has 6 different possible values it can show. Then if you roll two dice, there are 6*6 = 36 possible combinations of numbers you can get.
Of these 36 combinations, there are 3 ways to roll a 4:
1 on the first die, 3 on the second
2 on both dice
3 on the first die, 1 on the second

Thus, you have a 3/36 = 1/12 chance of rolling a total value of 4. Thus, if you roll the dice 1000 times, you expect to get a sum of 4 1000/12 = 83 1/3 ~ 83 times.