The probability that number selected at random from the numbers 1,2,3,…,15 is a multiple of 4, is

Explanation

To find the probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, we can follow these steps:

### Step 1: Identify the total number of outcomes
The total numbers we are considering are from 1 to 15. Therefore, the total number of outcomes is:
\[ \text{Total outcomes} = 15 \]

### Step 2: Identify the favorable outcomes
Next, we need to find how many of these numbers are multiples of 4. The multiples of 4 within the range of 1 to 15 are:
- 4
- 8
- 12

Thus, the favorable outcomes (multiples of 4) are:
\[ \text{Favorable outcomes} = 3 \quad (\text{which are } 4, 8, \text{ and } 12) \]

### Step 3: Calculate the probability
The probability \( P \) of selecting a multiple of 4 is given by the formula:
\[ P(\text{multiple of 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{15} \]

### Step 4: Simplify the probability
Now, we can simplify the fraction:
\[ P(\text{multiple of 4}) = \frac{3}{15} = \frac{1}{5} \]

### Final Answer
The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4 is:
\[ \frac{1}{5} \]

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