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
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:
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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
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Identify the number of students who failed the test and did not complete the homework:
- This number is given directly in the table: 6
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Calculate the probability:
- Probability = (Number of students who failed the test and did not complete the homework) / (Total number of students)
- Probability = 6 / 27
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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 .
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