A die is rolled. Find the probability of getting:
a composite number.

Answer

To find the probability of getting a composite number when a die is rolled, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Sample Space**:
When a die is rolled, the possible outcomes (sample space) are the numbers 1, 2, 3, 4, 5, and 6.
- Sample Space (S) = {1, 2, 3, 4, 5, 6}

2. **Identify Composite Numbers**:
A composite number is a whole number greater than 1 that is not prime; it has more than two distinct positive divisors.
- The composite numbers from the sample space are 4 and 6.
- Composite Numbers = {4, 6}

3. **Count the Favorable Outcomes**:
From the sample space, we see that there are 2 favorable outcomes (4 and 6) that are composite numbers.

4. **Calculate the Total Outcomes**:
The total number of outcomes when rolling a die is 6 (the numbers 1 through 6).

5. **Calculate the Probability**:
The probability (P) of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Here, the number of favorable outcomes is 2 (for composite numbers) and the total outcomes is 6.
\[ P(\text{Composite Number}) = \frac{2}{6} = \frac{1}{3} \]

### Final Answer:
The probability of getting a composite number when a die is rolled is \(\frac{1}{3}\).

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