Question

in a math class with 28 students, a test was given the same day that an assignment was due. there were 18 students who passed the test and 20 students who completed the assignment. there were 6 students who failed the test and also did not complete the assignment. what is the probability that a student chosen randomly from the class failed the test and did not complete the assignment?

Explanation:

Step1: Find the number of students who failed the test and did not complete the assignment

Total students = 28. Students who passed the test = 18. So students who failed the test = $28 - 18 = 10$. Students who failed the test and completed the assignment = 6. So students who failed the test and did not complete the assignment = $10 - 6 = 4$? Wait, no, wait. Wait, the problem says: 18 passed the test, 20 completed the assignment, 6 failed and did not complete. Wait, maybe I misread. Let's re-express:

Wait, the problem: "In a math class with 28 students, a test was given the same day that an assignment was due. There were 18 students who passed the test and 20 students who completed the assignment. There were 6 students who failed the test and also did not complete the assignment. What is the probability that a student chosen randomly from the class failed the test and did not complete the assignment?" Wait, no, the question is: "What is the probability that a student chosen randomly from the class failed the test and did not complete the assignment?" Wait, but it says "There were 6 students who failed the test and also did not complete the assignment." Wait, maybe I misread. Wait, let's check again.

Wait, the problem statement: "There were 18 students who passed the test and 20 students who completed the assignment. There were 6 students who failed the test and also did not complete the assignment. What is the probability that a student chosen randomly from the class failed the test and did not complete the assignment?" Wait, no, the question is: "What is the probability that a student chosen randomly from the class failed the test and did not complete the assignment?" But it says "There were 6 students who failed the test and also did not complete the assignment." Wait, that can't be. Wait, maybe the numbers are: total students 28. Passed:18, so failed:28-18=10. Completed assignment:20, so not completed:28-20=8. Now, students who failed and did not complete: let's use set theory. Let F be failed, N be not completed. We know that |F ∩ N| =? Wait, the problem says "There were 6 students who failed the test and also did not complete the assignment." Wait, maybe the original problem was miswritten. Wait, no, the user's image: "There were 18 students who passed the test and 20 students who completed the assignment. There were 6 students who failed the test and also did not complete the assignment. What is the probability that a student chosen randomly from the class failed the test and did not complete the assignment?" Wait, but that would be 6/28 = 3/14. Oh! Wait, maybe I misread. The problem says: "There were 6 students who failed the test and also did not complete the assignment." So the number of students who failed and did not complete is 6. Total students 28. So probability is 6/28 = 3/14.

Wait, let's confirm:

Total students: 28.

Number of students who failed the test and did not complete the assignment: 6 (given).

So probability = number of favorable outcomes / total number of outcomes = 6/28 = 3/14.

Yes, that makes sense. So the probability is 3/14.

Answer:

$\frac{3}{14}$