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 does not have a dog has a cat?\n| |has a cat|does not have a cat|\n|--|--|--|\n|has a dog|13|2|\n|does not have a dog|5|7|

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 does not have a dog has a cat?\n| |has a cat|does not have a cat|\n|--|--|--|\n|has a dog|13|2|\n|does not have a dog|5|7|

Answer

Explanation:

Step1: Find number of students without a dog

The number of students without a dog is the sum of those without a dog and with a cat and those without a dog and without a cat. So, $5 + 7=12$.

Step2: Calculate the conditional - probability

The probability that a student who does not have a dog has a cat is the number of students without a dog and with a cat divided by the number of students without a dog. Using the formula for conditional probability $P(A|B)=\frac{n(A\cap B)}{n(B)}$, here $A$ is the event of having a cat and $B$ is the event of not having a dog. So the probability is $\frac{5}{12}$.

Answer:

$\frac{5}{12}$