A dice is tossed once and even number has come up. The probability that it is either 2 or 4 is

Options

A. `(1)/(3)`
B. `(2)/(3)`
C. `(1)/(2)`
D. `(3)/(4)`

Answer

To solve the problem, we need to determine the probability that when a die is tossed and an even number comes up, it is either a 2 or a 4.

### Step-by-Step Solution:

1. **Identify the Sample Space**:
When a die is tossed, the possible outcomes are {1, 2, 3, 4, 5, 6}.

2. **Identify the Even Numbers**:
The even numbers in the sample space are {2, 4, 6}.

3. **Count the Total Number of Even Outcomes**:
There are 3 even numbers: 2, 4, and 6.

4. **Identify the Favorable Outcomes**:
We are interested in the outcomes where the die shows either 2 or 4. The favorable outcomes are {2, 4}.

5. **Count the Favorable Outcomes**:
There are 2 favorable outcomes: 2 and 4.

6. **Calculate the Probability**:
The probability \( P \) that the outcome is either 2 or 4 given that an even number has come up is calculated using the formula:
\[ P(\text{2 or 4 | even}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of even outcomes}} = \frac{2}{3} \]

7. **Final Answer**:
Therefore, the probability that the number is either 2 or 4 is \( \frac{2}{3} \).