Question

in a class of 24 students, 9 have a cat and 13 have a dog. there are 7 students who have a cat and a dog. what is the probability that a student has a cat given that they have a dog?

Explanation:

Step1: Recall conditional probability formula

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

Step2: Define events

Let $A$ = has a cat, $B$ = has a dog. $n(A \cap B)=7$, $n(B)=13$.

Step3: Calculate probability

$P(A|B) = \frac{n(A \cap B)}{n(B)} = \frac{7}{13}$

Answer:

$\frac{7}{13}$