In a musical chairs game, a person has been advised to stop playing the music at any time within 40 seconds after its start. What is the probability that the music will stop within the first 15 seconds?

Options

A. `(3)/(8)`
B. `(2)/(8)`
C. `(3)/(7)`
D. `(1)/(8)`

Answer

To solve the problem, we need to determine the probability that the music will stop within the first 15 seconds of a total of 40 seconds.

### Step-by-step Solution:

1. **Identify the Total Outcomes**:
The total time duration for stopping the music is 40 seconds. Each second can be considered as a possible outcome for stopping the music.
- Total outcomes = 40 seconds

2. **Identify the Favorable Outcomes**:
We need to find the number of favorable outcomes where the music stops within the first 15 seconds. The favorable outcomes are the time intervals from 1 second to 15 seconds.
- Favorable outcomes = 15 seconds (1, 2, 3, ..., 15)

3. **Calculate the Probability**:
The probability (P) is calculated using the formula:
\[ P = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values we have:
\[ P = \frac{15}{40} \]

4. **Simplify the Probability**:
We can simplify the fraction:
\[ P = \frac{15 \div 5}{40 \div 5} = \frac{3}{8} \]

5. **Final Answer**:
The probability that the music will stop within the first 15 seconds is:
\[ \frac{3}{8} \]