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 dog also has a cat?
Has a cat Does not have a cat
Has a dog 8 10
Does not have a dog 3 6

Answer 1

To find the probability that a student who has a dog also has a cat, we can use the provided data from the table.

From the table:
- The number of students who have both a cat and a dog (Has a dog and Has a cat) = 8
- The number of students who have a dog but do not have a cat (Has a dog and Does not have a cat) = 10

To find the probability that a student who has a dog also has a cat, we can use the formula for conditional probability:

\[
P(\text{Has a cat | Has a dog}) = \frac{P(\text{Has a cat and Has a dog})}{P(\text{Has a dog})}
\]

1. **Number of students who have a dog**:
\[
P(\text{Has a dog}) = \text{(Has a dog and Has a cat)} + \text{(Has a dog and Does not have a cat)} = 8 + 10 = 18
\]

2. **Probability of having a cat given the student has a dog**:
\[
P(\text{Has a cat | Has a dog}) = \frac{8}{18} = \frac{4}{9}
\]

Thus, the probability that a student who has a dog also has a cat is:

\[
\frac{4}{9}
\]