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|8|3|\n|does not have a dog|9|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|8|3|\n|does not have a dog|9|7|

Answer

Explanation:

Step1: Find number of students without a dog

The number of students who do not have a dog is the sum of those who do not have a dog and have a cat and those who do not have a dog and do not have a cat. So, $9 + 7=16$.

Step2: Find number of students without a dog and with a cat

The number of students who do not have a dog and have a cat is 9.

Step3: Calculate the probability

The probability $P$ that a student who does not have a dog has a cat is given by the number of students without a dog and with a cat divided by the number of students without a dog. So, $P=\frac{9}{16}$.

Answer:

$\frac{9}{16}$