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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 passed the test or completed the homework?Passed the test Failed the testCompleted the homework 17 2Did not complete the homework 3 4

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 passed the test or completed the homework?Passed the test Failed the testCompleted the homework 17 2Did not complete the homework 3 4

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Solution

The first step is to understand the data given in the table. Here is the data:

  • 17 students passed the test and completed the homework.
  • 2 students failed the test but completed the homework.
  • 3 students passed the test but did not complete the homework.
  • 4 students neither passed the test nor completed the homework.

The total number of students in the class is the sum of all these categories, which is 17 + 2 + 3 + 4 = 26 students.

The event of a student passing the test or completing the homework includes the following categories:

  • Students who passed the test and completed the homework (17 students)
  • Students who failed the test but completed the homework (2 students)
  • Students who passed the test but did not complete the homework (3 students)

So, the total number of students who either passed the test or completed the homework is 17 + 2 + 3 = 22 students.

The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes. In this case, the probability that a student chosen randomly from the class passed the test or completed the homework is the number of students who passed the test or completed the homework (22 students) divided by the total number of students (26 students).

So, the probability is 22/26 = 0.846 or 84.6% when expressed as a percentage.

This problem has been solved

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