A dice is tossed . The probability of having a prime number greater than 2 on toss is

Options

A. `1//3`
B. `1//3`
C. `1//12`
D. `2//3`

Answer

To find the probability of rolling a prime number greater than 2 when tossing a die, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Sample Space**:
When a die is tossed, the possible outcomes (the sample space) are:
\[ S = \{1, 2, 3, 4, 5, 6\} \]

2. **Identify Prime Numbers**:
Next, we need to identify the prime numbers within the sample space. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The prime numbers in the sample space are:
\[ \text{Prime Numbers} = \{2, 3, 5\} \]

3. **Filter Prime Numbers Greater Than 2**:
We are interested in prime numbers that are greater than 2. From our list of prime numbers, we find:
\[ \text{Prime Numbers Greater than 2} = \{3, 5\} \]

4. **Count the Favorable Outcomes**:
The favorable outcomes (prime numbers greater than 2) are 3 and 5. Therefore, the number of favorable outcomes is:
\[ \text{Number of Favorable Outcomes} = 2 \]

5. **Count the Total Outcomes**:
The total number of outcomes when rolling a die is:
\[ \text{Total Outcomes} = 6 \]

6. **Calculate the Probability**:
The probability \( P \) of rolling a prime number greater than 2 is given by the formula:
\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{2}{6} \]

7. **Simplify the Probability**:
Simplifying \( \frac{2}{6} \) gives:
\[ P = \frac{1}{3} \]

### Final Answer:
The probability of rolling a prime number greater than 2 when tossing a die is:
\[ \frac{1}{3} \]

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