Question

question
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 dog given that they have a cat?
\t\thas a dog\tdoes not have a dog
has a cat\t9\t14
does not have a cat\t2\t5

Explanation:

Step1: Identify relevant groups

We need the number of students who have a dog and a cat (9) and the total number of students who have a cat (9 + 14 = 23).

Step2: Apply conditional probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Here, $A$ is "has a dog" and $B$ is "has a cat". So we calculate $\frac{9}{9 + 14}=\frac{9}{23}$.

Answer:

$\frac{9}{23}$