in a class of students, the following data table summarizes how many students have a cat or a dog. what is…
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?\n| |has a cat|does not have a cat|\n|--|--|--|\n|has a dog|9|2|\n|does not have a dog|14|5|
Answer
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 $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of students who have both a cat and a dog, and $n(B)$ is the number of students who have a cat.
Step2: Identify $n(A\cap B)$ and $n(B)$ from the table
From the table, the number of students who have both a cat and a dog $n(A\cap B) = 9$. The number of students who have a cat is $n(B)=9 + 14=23$.
Step3: Calculate the conditional probability
$P(A|B)=\frac{n(A\cap B)}{n(B)}=\frac{9}{23}$.
Answer:
$\frac{9}{23}$