in a class of students, the following data table summarizes how many students have a cat or a dog. what is…

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of this problem, let $A$ be the event that a student has a dog and $B$ be the event that a student has a cat. Then $P(A\cap B)$ is the probability that a student has both a cat and a dog, and $P(B)$ is the probability that a student has a cat.

Step2: Calculate $P(A\cap B)$ and $P(B)$

The number of students who have both a cat and a dog is $n(A\cap B) = 4$. The number of students who have a cat is $n(B)=4 + 2=6$. The probability $P(A\cap B)=\frac{4}{4 + 2+5 + 11}=\frac{4}{22}$, and $P(B)=\frac{4 + 2}{4 + 2+5 + 11}=\frac{6}{22}$.

Step3: Calculate $P(A|B)$

Using the conditional - probability formula $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{\frac{4}{22}}{\frac{6}{22}}=\frac{4}{6}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$