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

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

Explanation:

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

`P(B|A) = (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) = (12)/(27)`

5 students who have a cat and a dog.

This means that
`P(A \cap B) = (5)/(27)`

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

`P(B|A) = ((5)/(27))/((12)/(27)) = (5)/(12) = 0.4167`

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