A health instructor surveyed all her students, and tallied the results. The first survey question asked, "Do you adhere to a vegetarian diet or omnivorous diet?" The second question asked, "Approximately how often do you exercise?"

To find the probability that a randomly selected student exercises daily and adheres to an omnivorous diet, we need to first determine the total number of students and the number of students that meet both criteria.

From the survey results:

• The number of students that adhere to a vegetarian diet and exercise daily: 2
• The number of students that adhere to an omnivorous diet and exercise daily: 1
• The number of students that adhere to a vegetarian diet and exercise weekly: 4
• The number of students that adhere to an omnivorous diet and exercise weekly: 3

Now we can summarize this into a table:

\[ \begin{array}{|c|c|c|} \hline & \text{Vegetarian Diet} & \text{Omnivorous Diet} \ \hline \text{Daily Exercise} & 2 & 1 \ \text{Weekly Exercise} & 4 & 3 \ \hline \end{array} \]

Next, we will compute the total number of students:

Total daily exercise students = 2 (vegetarian) + 1 (omnivorous) = 3
Total weekly exercise students = 4 (vegetarian) + 3 (omnivorous) = 7

So, the total number of students = Total daily + Total weekly = 3 + 7 = 10.

Now we determine the number of students exercising daily and adhering to an omnivorous diet, which is 1 (the value from the table).

To find the probability \( P \) that a randomly selected student exercises daily and adheres to an omnivorous diet, we use the formula:

\[ P(\text{Daily and Omnivorous}) = \frac{\text{Number of students who exercise daily and are omnivorous}}{\text{Total number of students}} = \frac{1}{10}. \]

Thus, the probability is \(\frac{1}{10}\).