90.2k views
2 votes
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?

User Sabahattin
by
7.9k points

1 Answer

4 votes

Answer:

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

User Enbr
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories