In a single throw of a dice, find the probability of getting a number :
(ii) less than or equal to 2

Answer

To find the probability of getting a number less than or equal to 2 in a single throw of a dice, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Sample Space**:
The sample space for a single throw of a dice consists of all the possible outcomes. A standard dice has 6 faces, numbered from 1 to 6.
- Sample Space (S) = {1, 2, 3, 4, 5, 6}

2. **Count the Total Outcomes**:
The total number of outcomes when throwing a dice is the number of faces on the dice.
- Total Outcomes = 6

3. **Identify the Favorable Outcomes**:
We need to find the outcomes that are less than or equal to 2. The numbers that satisfy this condition are 1 and 2.
- Favorable Outcomes = {1, 2}

4. **Count the Favorable Outcomes**:
The number of favorable outcomes is the count of the numbers that are less than or equal to 2.
- Number of Favorable Outcomes = 2 (which are 1 and 2)

5. **Calculate the Probability**:
The probability (P) of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values we have:
\[ P(\text{Getting a number less than or equal to 2}) = \frac{2}{6} \]

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

### Final Answer:
The probability of getting a number less than or equal to 2 in a single throw of a dice is \(\frac{1}{3}\).

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