Question

A fair 6-sided die is rolled three times. Find the probability that the sum of the three dice is 4 ?

Answer 1

`P("sum of 4") = 1/72`

Explanation:

Since the die is a 6-sided die (described as being "fair", meaning all possible outcomes from 1 to 6 are equally possible/probable), we know that overall there are `6^3 = 6*6*6 = 216` possible outcomes.

Now we want to enumerate all of the outcomes that result in a sum of 4. Since we're getting a minimum of 1 on each die (which gives us a total of 3), the only way we can get a sum of 4 on three rolls of a die is if we have a set of 1, 1, and 2. This means one of the die rolls will be a 2. Since we're rolling three times, there's three possibilities:

{1,1,2}, {1,2,1}, {2, 1, 1}

Thus, the probability is `3/216 = 1/72`