Let's carefully solve the given problem step by step.
### Step 1: Identify the Range of Integers
We are given that the integers range from 10 to 25, inclusive. First, we find out how many integers are within this range. To do this, subtract the smallest integer from the largest integer and then add 1:
[tex]\[
25 - 10 + 1 = 16
\][/tex]
So, there are 16 integers in total from 10 to 25.
### Step 2: Identify the Probability of Choosing a Specific Number
When choosing a number at random from a set of numbers, the probability of choosing any specific number is given by:
[tex]\[
\text{Probability} = \frac{\text{Number of desired outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
Here, the total number of possible outcomes is 16 (the total number of integers from 10 to 25).
### Step 3: Evaluate the Given Choices
We are given four choices for the probability:
- [tex]\[\frac{2}{25}\][/tex]
- [tex]\[\frac{3}{25}\][/tex]
- [tex]\[\frac{2}{16}\][/tex]
- [tex]\[\frac{3}{16}\][/tex]
### Step 4: Determine the Correct Probability
Since we want to find the probability with the total number of possible outcomes being 16, let’s examine the choices:
1. [tex]\[\frac{2}{25}\][/tex]: This implies 2 successful outcomes out of 25 total outcomes, which is not correct since our total number of outcomes is 16.
2. [tex]\[\frac{3}{25}\][/tex]: Similarly, this implies 3 out of 25 which doesn't match our total number of outcomes.
3. [tex]\[\frac{2}{16}\][/tex]: This implies 2 successful outcomes out of 16 total outcomes, which aligns with our context of having 16 total numbers.
4. [tex]\[\frac{3}{16}\][/tex]: This implies 3 successful outcomes out of 16 total outcomes, which also aligns with our context.
Given these interpretations, let's focus on the most relevant context-provided clue. Among the probabilities mentioned, [tex]\(\frac{2}{16}\)[/tex] appears to be the one matching directly with a context where we have 16 elements and 2 successful outcomes.
### Step 5: Confirm Correct Answer
The correct probability is, therefore, [tex]\(\frac{2}{16}\)[/tex]. This simplifies further to [tex]\(\frac{1}{8}\)[/tex], which corresponds to the probability of 0.125 or 12.5%.
Thus, the correct option is:
[tex]\(\frac{2}{16}\)[/tex]
Therefore, the answer is:
[tex]\(\boxed{3}\)[/tex]
