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 multiple of 3 ?

Answer

To solve the problem of finding the probability of selecting a counter that is a multiple of 3 from a set of counters numbered from 2 to 10, we can follow these steps:

### Step 1: Identify the total number of counters
The counters are numbered from 2 to 10. Therefore, the counters are:
- 2, 3, 4, 5, 6, 7, 8, 9, 10

**Total number of counters = 9**

### Step 2: Identify the favorable outcomes
Next, we need to find the counters that are multiples of 3 within the range of 2 to 10. The multiples of 3 in this range are:
- 3 (3 x 1)
- 6 (3 x 2)
- 9 (3 x 3)

**Favorable outcomes (multiples of 3) = 3, 6, 9**

**Total favorable outcomes = 3**

### Step 3: Calculate the probability
Probability is calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:
\[ \text{Probability} = \frac{3}{9} \]

### Step 4: Simplify the fraction
Now, we simplify the fraction:
\[ \frac{3}{9} = \frac{1}{3} \]

### Final Answer
The probability of selecting a counter that is a multiple of 3 is:
\[ \frac{1}{3} \]

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