A dice is thrown the probability of the event that either en even number appears or odd number appears is

Options

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

Answer

To solve the problem, we need to determine the probability of the event that either an even number appears or an odd number appears when a die is thrown.

### Step-by-Step Solution:

1. **Identify the Sample Space**:
When a die is thrown, the possible outcomes (sample space) are {1, 2, 3, 4, 5, 6}.

2. **Count the Total Outcomes**:
The total number of outcomes when throwing a die is 6 (the numbers 1 through 6).

3. **Identify Even and Odd Numbers**:
- Even numbers on a die: {2, 4, 6}
- Odd numbers on a die: {1, 3, 5}

4. **Count the Favorable Outcomes**:
- The event of getting an even number has 3 favorable outcomes (2, 4, 6).
- The event of getting an odd number also has 3 favorable outcomes (1, 3, 5).

5. **Combine the Events**:
Since every number on the die is either even or odd, the event of getting an even number or an odd number covers all possible outcomes. Therefore, the total number of favorable outcomes for the event "either an even number or an odd number" is 6.

6. **Calculate the Probability**:
The probability of an event is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
Here, the number of favorable outcomes is 6 (all outcomes) and the total number of possible outcomes is also 6. Thus,
\[ P(E) = \frac{6}{6} = 1 \]

### Final Answer:
The probability of the event that either an even number appears or an odd number appears when a die is thrown is **1**.