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
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] 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 [tex]P(A) = \frac{12}{27}[/tex]
5 students who have a cat and a dog.
This means that [tex]P(A \cap B) = \frac{5}{27}[/tex]
What is the probability that a student has a dog given that they have a cat?
[tex]P(B|A) = \frac{\frac{5}{27}}{\frac{12}{27}} = \frac{5}{12} = 0.4167[/tex]
41.67% probability that a student has a dog given that they have a cat
