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 has a dog given that they do not have a cat?\n| |has a cat|does not have a cat|\n|--|--|--|\n|has a dog|3|10|\n|does not have a dog|6|2|

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 has a dog given that they do not have a cat?\n| |has a cat|does not have a cat|\n|--|--|--|\n|has a dog|3|10|\n|does not have a dog|6|2|

Answer

Explanation:

Step1: Identify relevant numbers

We want the probability of having a dog given no cat. The number of students with no cat and a dog is 10, and the number of students with no cat is (10 + 2=12).

Step2: 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 having a dog and (B) is not having a cat, the probability (P=\frac{\text{Number of students with no cat and a dog}}{\text{Number of students with no cat}}). So (P=\frac{10}{12}=\frac{5}{6}).

Answer:

(\frac{5}{6})