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 who has a dog also has a cat?\n| |has a cat|does not have a cat|\n|--|--|--|\n|has a dog|2|5|\n|does not have a dog|3|13|

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 who has a dog also has a cat?\n| |has a cat|does not have a cat|\n|--|--|--|\n|has a dog|2|5|\n|does not have a dog|3|13|

Answer

Explanation:

Step1: Find number of students with a dog

Add the number of students who have a dog and a cat and those who have a dog but no cat. So, $2 + 5=7$.

Step2: Find number of students with a dog and a cat

From the table, the number of students with a dog and a cat is 2.

Step3: Calculate the conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $A$ is the event of having a cat and $B$ is the event of having a dog, the probability that a student who has a dog also has a cat is $\frac{\text{Number of students with a dog and a cat}}{\text{Number of students with a dog}}$. So, the probability is $\frac{2}{7}$.

Answer:

$\frac{2}{7}$