Question

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 completed the homework?
Passed the test Failed the test
Completed the homework 9 4
Did not complete the homework 2 6

Answer 1

We want P(passed | completed) = (number who passed and completed) / (number who completed) = 9 / (9+4) = 9/13 ≈ 0.6923 (about 69.2%).