A fair die is rolled. Find the probability of throwing a number less than 3 .

To find the probability of throwing a number less than 3 when rolling a fair die, we can follow these steps: 1. **Identify the total number of outcomes**: A fair die has 6 faces, numbered from 1 to 6. Therefore, the total number of possible outcomes when rolling the die is 6. 2. **Identify the favorable outcomes**: The numbers less than 3 on a die are 1 and 2. Thus, the favorable outcomes are: - 1 - 2 This gives us a total of 2 favorable outcomes. 3. **Calculate the probability**: The probability \( P \) of an event is given by the formula: \[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] Substituting the values we have: \[ P = \frac{2}{6} \] 4. **Simplify the fraction**: \[ P = \frac{1}{3} \] Thus, the probability of throwing a number less than 3 when rolling a fair die is \( \frac{1}{3} \).