A dice is thrown once. Find the probability of getting :
a number greater than 4

Answer

To solve the problem of finding the probability of getting a number greater than 4 when a dice is thrown once, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Sample Space**:
When a dice is thrown, the possible outcomes (sample space) are:
\[ S = \{1, 2, 3, 4, 5, 6\} \]
This means there are a total of 6 possible outcomes.

**Hint**: Remember that the sample space of a dice includes all the numbers from 1 to 6.

2. **Determine the Favorable Outcomes**:
We need to find the outcomes that are greater than 4. The numbers greater than 4 in our sample space are:
\[ \{5, 6\} \]
Therefore, the favorable outcomes are 5 and 6, which gives us a total of 2 favorable outcomes.

**Hint**: List out the numbers in the sample space and identify which ones meet the condition of being greater than 4.

3. **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:
\[ P(\text{number greater than 4}) = \frac{2}{6} \]

4. **Simplify the Probability**:
We can simplify \( \frac{2}{6} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[ P(\text{number greater than 4}) = \frac{1}{3} \]

5. **Final Answer**:
Thus, the probability of getting a number greater than 4 when a dice is thrown once is:
\[ \frac{1}{3} \]

### Summary:
The probability of rolling a number greater than 4 on a single throw of a dice is \( \frac{1}{3} \).