My locker combination has three digits. None of the digits are 0. What is the probability that the first digit of my locker combination is less than 3?

To find the probability, we need to determine the number of favorable outcomes (the first digit being less than 3) and divide it by the total number of possible outcomes.

Since none of the digits can be 0, the possible digits for each digit in the combination are 1-9.

To find the number of favorable outcomes, we consider all the combinations where the first digit is less than 3. These combinations are: 1XX, 2XX. For each case, the second and third digits can take any value from 0-9 (except 0).

For 1XX: There are 9 choices for the second digit (1-9) and 9 choices for the third digit (1-9), giving a total of 9 * 9 = 81 combinations.
For 2XX: Similarly, there are 9 choices for the second digit (1-9) and 9 choices for the third digit (1-9), giving a total of 9 * 9 = 81 combinations.

Therefore, the total number of favorable outcomes is 81 + 81 = 162.

To find the total number of possible outcomes, we consider all the combinations where each digit in the combination can be any digit from 1-9 (excluding 0). Therefore, the total number of outcomes is 9 * 9 * 9 = 729.

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes
= 162 / 729
= 0.222 or 22.2%

So, the probability that the first digit of your locker combination is less than 3 is approximately 0.222 or 22.2%.