Nine counters numbered 2 to 10 are put in a bag . One counter is selected at random . What is the probility of getting a counter with :
a square number

Answer

To solve the problem, we need to find the probability of selecting a counter with a square number from a set of counters numbered from 2 to 10.

### Step-by-Step Solution:

1. **Identify the Total Outcomes**:
The counters are numbered from 2 to 10. Therefore, the total number of counters is:
\[ \text{Total outcomes} = 10 - 2 + 1 = 9 \]

2. **List the Square Numbers**:
We need to identify which numbers between 2 and 10 are perfect squares. The perfect squares in this range are:
- \(2^2 = 4\)
- \(3^2 = 9\)

Thus, the perfect squares from the counters are 4 and 9.

3. **Count the Favorable Outcomes**:
The favorable outcomes (the counters that are square numbers) are:
- 4
- 9

Therefore, the number of favorable outcomes is:
\[ \text{Favorable outcomes} = 2 \quad (\text{which are } 4 \text{ and } 9) \]

4. **Calculate the Probability**:
The probability \(P\) of selecting a counter with a square number is given by the formula:
\[ P(\text{square number}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{2}{9} \]

### Final Answer:
The probability of getting a counter with a square number is \(\frac{2}{9}\).

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