Question

In a class 27 of students, 12 have a cat and 11 have a dog. There are 5 students who have a cat and a dog. What is the probability that a student has a dog given that they have a cat?

Answer 1

Answer:

41.67% probability that a student has a dog given that they have a cat

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: having a cat.

Event B: having a dog.

12 of 27 students have a cat:

This means that $P(A) = \frac{12}{27}$

5 students who have a cat and a dog.

This means that $P(A \cap B) = \frac{5}{27}$

What is the probability that a student has a dog given that they have a cat?

$P(B|A) = \frac{\frac{5}{27}}{\frac{12}{27}} = \frac{5}{12} = 0.4167$

41.67% probability that a student has a dog given that they have a cat