In a math class with 27 students, a test was given the same day that an assignment was due. There were 20 students who passed the test and 18 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 failed the test given that they completed the assignment?
Question
In a math class with 27 students, a test was given the same day that an assignment was due. There were 20 students who passed the test and 18 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 failed the test given that they completed the assignment?
Solution
To solve this problem, we need to use the concept of conditional probability.
Step 1: Identify the relevant information from the problem.
- Total number of students = 27
- Number of students who passed the test = 20
- Number of students who completed the assignment = 18
- Number of students who both passed the test and completed the assignment = 16
Step 2: Calculate the number of students who completed the assignment but failed the test. This is the number of students who completed the assignment minus the number of students who both passed the test and completed the assignment. So, 18 (completed the assignment) - 16 (passed the test and completed the assignment) = 2 students completed the assignment but failed the test.
Step 3: Calculate the conditional probability. The probability that a student failed the test given that they completed the assignment is the number of students who completed the assignment but failed the test divided by the total number of students who completed the assignment. So, the probability = 2 (completed the assignment but failed the test) / 18 (completed the assignment) = 1/9.
So, the probability that a student failed the test given that they completed the assignment is 1/9.
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