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 who completed the assignment passed the test? Answer:

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Total Students Count: First, let's determine the total number of students who either passed the test or completed the assignment, or both. We know that 4 students neither passed the test nor completed the assignment. Since there are 19 students in total, this means that 19 - 4 = 15 students either passed the test, completed the assignment, or did both.Find Students Both Passed and Completed: Next, we need to find out how many students both passed the test and completed the assignment. We can use the principle of inclusion-exclusion for this. The formula is: Number who did both = (Number who passed the test) + (Number who completed the assignment) - (Total number who passed the test or completed the assignment or both)Calculate Number Who Did Both: Now we plug in the numbers we have: Number who did both = 12 + 13 - 15Calculate Probability: Calculating the number who did both gives us: Number who did both = 25 - 15 Number who did both = 10 So, there are 10 students who both passed the test and completed the assignment.Calculate Probability: The probability that a student who completed the assignment passed the test is the number of students who did both divided by the number of students who completed the assignment. Probability = Number who did both / Number who completed the assignmentFinal Probability: Plugging in the numbers we have: Probability = 10 / 13The fraction 10/13 cannot be simplified further, so this is the final probability.

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