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 cat also has a dog?\n| |has a cat|does not have a cat|\n|--|--|--|\n|has a dog|9|10|\n|does not have a dog|6|4|

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 cat also has a dog?\n| |has a cat|does not have a cat|\n|--|--|--|\n|has a dog|9|10|\n|does not have a dog|6|4|

Answer

Explanation:

Step1: Find number of students with a cat

We add the number of students who have a cat and have a dog and those who have a cat and don't have a dog. So, $9 + 6=15$.

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

From the table, the number of students with both a cat and a dog is 9.

Step3: Calculate 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 dog and $B$ is the event of having a cat, the probability that a student who has a cat also has a dog is $\frac{\text{Number of students with both cat and dog}}{\text{Number of students with a cat}}$. So, the probability is $\frac{9}{15}=\frac{3}{5}=0.6$.

Answer:

$0.6$