Problem
In a math class with 19 students, a test was given the same day that an assignment was due. There were 12 students who passed the test and 13 students who completed the assignment. There were 4 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?
Solution
Step 1 ：\( P(T) = \frac{12}{19} \)
Step 2 ：\( P(A \cap T) = \frac{12 + 13 - 19 + 4}{19} = \frac{10}{19} \)
Step 3 ：\( P(A|T) = \frac{P(A \cap T)}{P(T)} = \frac{10/19}{12/19} \)
