Question

If three fair 6-sided dice are rolled, what is the probability that all three numbers wil be the same?

Answer 1

1 in 36, and here's why...

There are a total of 216 possible rolls: 6 on the first die, 6 on the second die, and 6 on the third die. We can list them as (first, second, third); for example, (1, 3, 2) means a 1 on the first die, 3 on the second, and 2 on the last.



There are only six possible rolls where all three numbers are the same: (1, 1, 1), (2, 2, 2), (3, 3, 3), (4, 4, 4), (5, 5, 5), and (6, 6, 6). The other 210 possible rolls don't match, so the ones that do match represent 6 out of 216, or 1 out of 36. Since probabilities are usually written as reduced fractions, we would say that the probability is 1/36 or 1 in 36.