All possible 3-digit numbers made with only the digits 1 and 2 are written on separate pieces of paper. Without looking, Liam takes one piece. What is the probability that the number on the paper will use just one digit?

To find the probability you need to know the number of desired outcomes (i. e. one digit only used) and the total number of outcomes.

In this case there are 3 desired outcomes - 111, 222, 333.

Since any of the 3 positions in the 3-digit number can be any of 3 numbers, there are 3 x 3 x 3 = 27 total possible outcomes.

The probability of having a desired outcome is 3 / 27 = 1 / 9 = 11.1%