Question

In a math class with 30 students, a test was given the same day that an assignment was due. There were 21 students who passed the test and 20 students who completed the assignment. There were 7 students who failed the test and also did not complete the assignment. What is the probability that a student completed the homework given that they passed the test?

Answer 1

"Given that they passed the test" says we're only considering the 21 students who passed the test.

There were 9 students who didn't pass the test and 7 of those didn't complete the HW. This means that 2 students who did the HW didn't pass the test.

Since 20 students completed the HW and 2 didn't pass the test, 18 students completed the HW and passed the test.

18/21 = 6/7 or 85.71%

Your probability is 85.71%.