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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 has a cat given that they have a dog?
Has a cat Does not have a cat
Has a dog 3 17
Does not have a dog 4 5
Answer
Attempt 1 out of 2

Answer 1

To determine the probability that a student has a cat given that they have a dog, we can use the conditional probability formula:

\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\]

Where:
- \( A \) is the event that a student has a cat.
- \( B \) is the event that a student has a dog.

From the data table, we can gather the following information:

- Students who have both a cat and a dog: 3
- Students who have a dog (with or without a cat): 3 (with a cat) + 17 (without a cat) = 20

Now we can plug these numbers into the conditional probability formula:

\[
P(A|B) = \frac{\text{Number of students with both a cat and a dog}}{\text{Total number of students with a dog}} = \frac{3}{20}
\]

Therefore, the probability that a student has a cat given that they have a dog is:

\[
P(A|B) = \frac{3}{20}
\]

This simplifies to 0.15, or 15%.