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 cat given that they do not have a dog?Has a cat Does not have a catHas a dog 5 4Does not have a dog 8 7
Question
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 cat given that they do not have a dog?Has a cat Does not have a catHas a dog 5 4Does not have a dog 8 7
Solution
To solve this problem, we need to focus on the students who do not have a dog. According to the table, there are 8 students who have a cat and do not have a dog, and 7 students who do not have a cat or a dog.
So, the total number of students who do not have a dog is 8 (those who have a cat) + 7 (those who do not have a cat) = 15.
The probability that a student has a cat given that they do not have a dog is therefore the number of students who have a cat and do not have a dog divided by the total number of students who do not have a dog.
So, the probability = 8 (students who have a cat and do not have a dog) / 15 (total students who do not have a dog) = 0.53 (rounded to two decimal places).
So, the probability that a student has a cat given that they do not have a dog is 0.53 or 53%.
Similar Questions
In a class of 18 students, 7 have a cat and 12 have a dog. There are 2 students who do not have a cat or a dog. What is the probability that a student who has a cat also has a dog?
In a class of students, the following data table summarizes the gender of the students and whether they have an A in the class. What is the probability that a student has an A given that the student is female?Female MaleHas an A 16 4Does not have an A 2 8
In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student has a brother given that they do not have a sister?Has a brother Does not have a brotherHas a sister 2 10Does not have a sister 9 6
In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class does not play an instrument?Plays an instrument Does not play an instrumentPlays a sport 5 3Does not play a sport 9 12
In a class of students, the following data table summarizes how many students passed a test and completed the homework due the day of the test. What is the probability that a student passed the test given that they did not complete the homework?Passed the test Failed the testCompleted the homework 9 3Did not complete the homework 4 6
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.