To solve this probability problem, we'll follow a few basic steps related to simple probability.
Step 1: Define the total number of possible outcomes.
When rolling a fair six-sided die, there are 6 possible outcomes, since the die has 6 faces numbered from 1 to 6.
Step 2: Identify the favorable outcomes.
In this case, we're looking for the probability of rolling a number less than 4. The numbers less than 4 on a six-sided die are 1, 2, and 3.
Step 3: Count the number of favorable outcomes.
We've already listed the favorable outcomes (1, 2, and 3), which amounts to 3 favorable outcomes.
Step 4: Calculate the probability.
The probability \( P \) of an event is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
Applying the formula to our scenario:
\[ P(\text{Rolling a number less than 4}) = \frac{3}{6} \]
Step 5: Simplify the fraction (if possible).
\[ P(\text{Rolling a number less than 4}) = \frac{3}{6} = \frac{1}{2} \]
So the probability of rolling a number less than 4 on a fair six-sided die is \( \frac{1}{2} \) or 0.5, which means there is a 50% chance of this event occurring.
