Question

You are going to roll two dice. Let the variable x = the sum of the numbers rolled. What is the probability that x = 9 ?

Answer 1

Assuming these are two six-sided dice, you'll have 36 total combinations to test out. To get the 36, I just multiplied the 6 sides on both dice (6x6=36). First you have to test out all the possible combinations. Making it easier for you, I'll just list the ones that work. The combinations that work are 3+6, 4+5, 5+4, and 6+3. This means there are 4 combinations that work out of 36. This gives us the fraction 4/36. Now, this needs to be simplified. Both numbers are divisible by four, so we'll divide by four. The new fraction is 1/9, which is your answer. This means that, statistically speaking, if you rolled those two dice nine times, the sum of the numbers would be 9 only once. You have an 11% chance of having two numbers on the dice that have a sum of 9.

Answer 2

Explanation:

We assume a dice that is a perfect cube, so every side have equal oportunity to be rolled. For each roll we have 6 possibilities, so we have in total 6 rolls x 6 rolls: 36 possibilities, the sum of this rolls is showed in the adjunt table:

The sums in red are the only that sums 9, there is only 4 possibilites in all the 36 possibilites that sums 9, so the probability of this is 4 possibilties / 36 possibilities = 1/9