# If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled?

**Solution:**

Given a fair die is rolled three times.

A fair die has 6 faces, hence, the sample space will be {1, 2, 3, 4, 5, 6}

So, on rolling a die thrice, the number of elements in sample space is 6^{3} = 216

Let us assume that the die in the first roll shows 3, hence the second die and third die can show any of the other 5 numbers.

First, the probability of rolling a single value (in this case 3) on a fair 6-sided die would be one out of six.

The probability of NOT rolling that number would be five out of six.

Let P be the probability of getting 3 only once

P= 1/ 6 × 5/6 × 5/6 = 25/216

The number 3 can be showed in any of the three dies at a time

Hence required probability = 25/216 + 25/216 + 25/216 = 75/216 = 25/72

P = 25/72

Therefore, the probability that exactly one 3 is rolled is 25/72.

## If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled?

**Summary:**

If a fair 6-sided die is rolled three times, then the probability that exactly one 3 is rolled is 25/72.