A die is rolled. Find the probability of getting:
a multiple of 3.

Answer

To solve the problem of finding the probability of getting a multiple of 3 when a die is rolled, we can follow these steps:

### Step 1: Identify the Sample Space
The sample space for rolling a die consists of all possible outcomes. A standard die has six faces, numbered from 1 to 6. Therefore, the sample space \( S \) is:
\[ S = \{1, 2, 3, 4, 5, 6\} \]

### Step 2: Count the Total Number of Outcomes
The total number of outcomes when rolling a die is the number of elements in the sample space. Since there are 6 faces on the die:
\[ \text{Total outcomes} = 6 \]

### Step 3: Identify the Favorable Outcomes
Next, we need to find the outcomes that are multiples of 3. The multiples of 3 within the range of the die's faces are:
- 3 (since \( 3 \times 1 = 3 \))
- 6 (since \( 3 \times 2 = 6 \))

Thus, the favorable outcomes are:
\[ \{3, 6\} \]

### Step 4: Count the Favorable Outcomes
Now, we count the number of favorable outcomes:
\[ \text{Favorable outcomes} = 2 \] (which are 3 and 6)

### Step 5: Calculate the Probability
The probability \( P \) of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:
\[ P(\text{multiple of 3}) = \frac{2}{6} = \frac{1}{3} \]

### Final Answer
The probability of rolling a multiple of 3 when a die is rolled is:
\[ \frac{1}{3} \]

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