Question

In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student who has a cat also has a dog?
Has a cat Does not have a cat
Has a dog 2 3
Does not have a dog 14 10
Answer

Answer 1

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 \(\frac{1}{8}\).