In a math class with 28 students, a test was given the same day that an assignment was due. There were 20 students who passed the test and 19 students who completed the assignment. There were 16 students who passed the test and also completed the assignment. What is the probability that a student passed the test given that they completed the homework?

In a math class with 28 students, a test was administered the same day an assignment was due. There were 20 students who passed the test and 19 students who completed the assignment. There were 16 students who passed the test and also completed the assignment. What is the probability that a student will pass the test knowing that he has done his homework? draw a venn diagram

test passed ---- both - did assignment

20-16=4 -------- 16 -------- 19-16 = 3

4 + 16 + 3 = 23 who did something useful

this leaves 28 - 23 = 5 out of your diagram which did nothing

16 of the 19 who did the homework passed the test

then

16/19 = 0.842

Doing the homework seems to have helped them pass the test.