Question

In a math class with 21 students, a test was given the same day that an assignment was due. There were 13 students who passed the test and 12 students who completed the assignment. There were 10 students who passed the test and also completed the assignment. What is the probability that a student completed the assignment given that they failed the test?

Answer 1

To find the probability, calculate the number of students who completed the assignment and failed the test (2) and divide it by the number of students who failed the test (8). This gives us a probability of 1/4, or 25%.

Step-by-step explanation:

To calculate the probability that a student completed the assignment given that they failed the test, we first need to identify the students who failed the test. Since there are 21 students and 13 students passed the test, there are 21 - 13 = 8 students who failed the test. We are told that 10 students passed the test and also completed the assignment, which implies that there are 12 - 10 = 2 students who completed the assignment but did not pass the test.

So, among the 8 students who failed the test, 2 students completed the assignment. The probability is calculated by dividing the number of students who completed the assignment and failed the test by the total number of students who failed the test.

The probability is therefore 2/8, which simplifies to 1/4 or 0.25. So, there is a 25% chance that a student completed the assignment given that they failed the test.