To find the probability that a student who has a cat also has a dog, we need to first identify the relevant counts from the data table provided:
- Students who have both a cat and a dog: 2
- Students who have a cat but do not have a dog: 14
Now, we can sum these two numbers to find the total number of students who have a cat:
\[ \text{Total students with a cat} = \text{(Students with a cat and a dog)} + \text{(Students with a cat and without a dog)} = 2 + 14 = 16 \]
The probability that a student who has a cat also has a dog can be calculated using the formula:
\[ P(\text{Has a dog} \mid \text{Has a cat}) = \frac{\text{Number of students with a cat and a dog}}{\text{Total number of students with a cat}} \]
So we have:
\[ P(\text{Has a dog} \mid \text{Has a cat}) = \frac{2}{16} = \frac{1}{8} \]
Thus, the probability that a student who has a cat also has a dog is \(\frac{1}{8}\).