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 cat given that they have a dog?\n| |has a cat|does not have a cat|\n|--|--|--|\n|has a dog|2|3|\n|does not have a dog|7|18|
Answer
Explanation:
Step1: Recall conditional - probability formula
The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of frequency, if $A$ is the event of having a cat and $B$ is the event of having a dog, $P(A|B)=\frac{n(A\cap B)}{n(B)}$, 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 dog.
Step2: Identify relevant values from the table
From the table, the number of students who have both a cat and a dog $n(A\cap B) = 2$, and the number of students who have a dog $n(B)=2 + 3=5$.
Step3: Calculate the probability
$P(A|B)=\frac{n(A\cap B)}{n(B)}=\frac{2}{5}=0.4$
Answer:
$0.4$