A die is thrown. What is the probability of getting an even number?

Options

A. `1/2`
B. `2/3`
C. `5/6`
D. `1/6`

Answer

To find the probability of getting an even number when a die is thrown, we can follow these steps:

### Step-by-Step Solution:

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

2. **Count the Total Outcomes**:
The total number of outcomes when throwing a die is the number of elements in the sample space, which is:
\[ \text{Total outcomes} = 6 \]

3. **Identify the Favorable Outcomes**:
We need to find the even numbers in the sample space. The even numbers between 1 and 6 are:
\[ \{2, 4, 6\} \]
So, the favorable outcomes (even numbers) are 2, 4, and 6.

4. **Count the Favorable Outcomes**:
The number of favorable outcomes (even numbers) is:
\[ \text{Favorable outcomes} = 3 \]

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:
\[ P(\text{even number}) = \frac{3}{6} \]

6. **Simplify the Probability**:
We can simplify \( \frac{3}{6} \) to:
\[ P(\text{even number}) = \frac{1}{2} \]

### Final Answer:
The probability of getting an even number when a die is thrown is:
\[ \frac{1}{2} \]