Apair of dice is rolled. what is the probability of getting a sum of 4

What are the possible ways you can get a sum of 4 when you roll a pair of dice (assuming these are 6-sided dice):

First Die  Second Die
     1              3
     2              2
     3              1

So, there are 3 ways to get a sum of 4.

Now, how many total possible outcomes are there when you roll a pair of dice? There are several ways to figure this out; I'm not sure which way(s) you've been taught. One way is to systematically write out all of the possible outcomes in a chart similar to the one I made above. Another way is to use the "Fundamental Counting Principle" which says that you can multiply the number of possible outcomes on the first die by the number of possible outcomes on the second die to get the total possible outcomes when the dice are rolled together.

Since there are 6 outcomes for the first die and 6 outcomes for the second, the total would be 6 * 6 = 36. There are 36 total possible outcomes when rolling 2 dice.

Finally, to get the probability, you need to set up the fraction

number of ways to get 4
--------------------------------
total possible outcomes

So we have:



which then reduces to



That's the probability of rolling a sum of four.