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|7|10|\n|does not have a dog|2|9|

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|7|10|\n|does not have a dog|2|9|

Answer

Explanation:

Step1: Identify relevant numbers

The number of students who have a dog and a cat is 7. The number of students who have a dog is (7 + 10=17).

Step2: Calculate conditional - probability

The formula for conditional probability (P(A|B)=\frac{P(A\cap B)}{P(B)}). In the context of this problem, if (A) is the event of having a cat and (B) is the event of having a dog, then the probability that a student who has a dog also has a cat is (\frac{\text{Number of students with both cat and dog}}{\text{Number of students with a dog}}). So the probability (P=\frac{7}{17}).

Answer:

(\frac{7}{17})