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In a math class with 20 students, a test was given the same day that an assignment was due. There were 10 students who passed the test and 14 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 passed the test given that they completed the assignment? Answer:

In a math class with 2020 students, a test was given the same day that an assignment was due. There were 1010 students who passed the test and 1414 students who completed the assignment. There were 44 students who failed the test and also did not complete the assignment. What is the probability that a student passed the test given that they completed the assignment?\newlineAnswer:

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Full solution

Q. In a math class with 2020 students, a test was given the same day that an assignment was due. There were 1010 students who passed the test and 1414 students who completed the assignment. There were 44 students who failed the test and also did not complete the assignment. What is the probability that a student passed the test given that they completed the assignment?\newlineAnswer:
  1. Identify Total Students: First, let's identify the total number of students who completed the assignment, which is given as 1414 students.
  2. Find Passing Students: Next, we need to find out how many students passed the test among those who completed the assignment. We know that 1010 students passed the test in total, and 44 students both failed the test and did not complete the assignment. This means that the number of students who passed the test but did not complete the assignment is the total number of students who passed the test minus the number of students who passed the test and completed the assignment.
  3. Calculate Students Passed: Since there are 2020 students in total and 44 students neither passed the test nor completed the assignment, the number of students who either passed the test or completed the assignment (or both) is 20−4=1620 - 4 = 16 students.
  4. Determine Probability: Now, we know that 1414 students completed the assignment. Since 1616 students either passed the test or completed the assignment, and 1010 students passed the test, we can use the principle of inclusion-exclusion to find the number of students who both passed the test and completed the assignment: 10+14−16=810 + 14 - 16 = 8 students.
  5. Calculate Probability: The probability that a student passed the test given that they completed the assignment is the number of students who both passed the test and completed the assignment divided by the total number of students who completed the assignment. So, the probability is 814\frac{8}{14}.
  6. Simplify Fraction: To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 22. So, 814\frac{8}{14} simplifies to 47\frac{4}{7}.

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