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In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class failed the test and did not complete the homework?Passed the test Failed the testCompleted the homework 14 3Did not complete the homework 4 6

Question

In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class failed the test and did not complete the homework?Passed the test Failed the testCompleted the homework 14 3Did not complete the homework 4 6

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Solution

To find the probability that a student chosen randomly from the class failed the test and did not complete the homework, follow these steps:

  1. Identify the total number of students in the class:

    • Students who passed the test and completed the homework: 14
    • Students who failed the test and completed the homework: 3
    • Students who passed the test and did not complete the homework: 4
    • Students who failed the test and did not complete the homework: 6

    Total number of students = 14 + 3 + 4 + 6 = 27

  2. Identify the number of students who failed the test and did not complete the homework:

    • This number is given directly in the table: 6
  3. Calculate the probability:

    • Probability = (Number of students who failed the test and did not complete the homework) / (Total number of students)
    • Probability = 6 / 27
  4. Simplify the fraction:

    • Simplify 6/27 by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
    • Probability = (6 ÷ 3) / (27 ÷ 3) = 2 / 9

Therefore, the probability that a student chosen randomly from the class failed the test and did not complete the homework is 29 \frac{2}{9} .

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