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In a class of students, the following data table summarizes how many student 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? & }(c) Passed the test & Failed the test Completed the homework & 12 & 6 Did not complete the homework & 3 & 4

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In a class of students, the following data table summarizes how many student 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?

 & }(c)
Passed the 
test
 & 
Failed the 
test
 
 Completed the homework & 12 & 6 
 
Did not complete the 
homework
 & 3 & 4

In a class of students, the following data table summarizes how many student 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? & }(c) Passed the test & Failed the test Completed the homework & 12 & 6 Did not complete the homework & 3 & 4

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VernonElite · Tutor for 8 years

Answer

To find the probability that a student chosen randomly from the class either passed the test or completed the homework, we need to consider the total number of students who either passed the test or completed the homework, and then divide that by the total number of students in the class.First, let's identify the number of students who passed the test, completed the homework, or both. According to the table:- 12 students passed the test and completed the homework.- 3 students passed the test but did not complete the homework.- 6 students failed the test but completed the homework.Now, let's calculate the total number of students who passed the test or completed the homework:\[\text{Total students who passed the test or completed homework} = \text{Passed test and completed homework} + \text{Passed test only} + \text{Completed homework only}\]\[= 12 + 3 + 6\]\[= 21\]Next, we need to find the total number of students in the class. We can do this by adding all the numbers in the table:\[\text{Total number of students} = 12 + 6 + 3 + 4\]\[= 25\]Now we can calculate the probability that a student chosen randomly from the class passed the test or completed the homework:\[P(\text{Passed test or completed homework}) = \frac{\text{Total students who passed the test or completed homework}}{\text{Total number of students}}\]\[= \frac{21}{25}\]\[= \frac{21}{25}\]So, the probability that a student chosen randomly from the class passed the test or completed the homework is \(\boxed{\frac{21}{25}}\).
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