Probability is largely about being able to count the possible outcomes. Using a standard six sided die is an excellent tool for learning the concept. Let’s assume we have a fair six-sided die. This means that there is an equal probability of landing on any of the six sides. Let’s ask the question, what is the probability of rolling a 3. There is only one way to get a 3 so we can say there is a 1 in 6 probability ( 1 / 6 = 16.66%).

Now let’s assume we have two dice, what is the probability of rolling a 3 (in other words, the sum of dice 1 and dice 2 equals 3. There are a couple of ways this could occur.

Die 1 = 2 Die 2 = 1

Die 2 = 1 Die 2 = 2

With 1 die, there are 6 possible outcomes. With 2 dice, there are 36 possible outcomes. The table below helps illustrate all the possible outcomes. We can simply count the number of times the 3 shows up, which is exactly two times. Thus the probability of rolling a 3 with two dice is 2 in 36 ( 2 / 36 = 0.55%)

Can you see which outcome is most likely? You can see on the diagonal rising from left to right is the number 7. There are 6 ways to roll a 7 with two dice and thus the probability of rolling a 7 is 6 in 36 (6 / 36 = 1 /6 = 16.66%)

Does this sound familiar? Yes, its related to the game of Craps and is the most common outcome in craps.