A number is selected from the numbers 1,2 …, 15. What is the probability that it is a multiple of 4?

Options

A. `(7)/(15)`
B. `(2)/(5)`
C. `(1)/(5)`
D. `(2)/(15)`

Answer

To solve the problem of finding the probability that a number selected from the set of numbers 1 to 15 is a multiple of 4, we can follow these steps:

### Step 1: Identify the total number of outcomes
The total number of outcomes is the total number of integers from 1 to 15. This can be calculated as follows:

Total outcomes = 15 (since we are considering the numbers 1, 2, 3, ..., 15)

### Step 2: Identify the favorable outcomes
Next, we need to find the numbers between 1 and 15 that are multiples of 4. The multiples of 4 in this range are:

- 4 (4 × 1)
- 8 (4 × 2)
- 12 (4 × 3)

So, the favorable outcomes are 4, 8, and 12.

### Step 3: Count the favorable outcomes
Now we count the favorable outcomes identified in Step 2:

Favorable outcomes = 3 (the numbers 4, 8, and 12)

### Step 4: Calculate the probability
The probability (P) of selecting a multiple of 4 can be calculated using the formula:

\[ P(\text{multiple of 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:

\[ P(\text{multiple of 4}) = \frac{3}{15} \]

### Step 5: Simplify the probability
Now we simplify the fraction:

\[ P(\text{multiple of 4}) = \frac{3}{15} = \frac{1}{5} \]

Thus, the probability that a number selected from 1 to 15 is a multiple of 4 is \( \frac{1}{5} \).

### Final Answer
The probability that a number selected from the numbers 1 to 15 is a multiple of 4 is \( \frac{1}{5} \).

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