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 completed the homework?
Passed the test Failed the test
Completed the homework 15 6
Did not complete the homework 2 4

Answer 1

To find the probability that a randomly chosen student completed the homework, we first need to determine the total number of students and the number of students who completed the homework.

From the table:
- Students who completed the homework and passed the test: 15
- Students who completed the homework and failed the test: 6
- Total students who completed the homework: \(15 + 6 = 21\)

- Students who did not complete the homework and passed the test: 2
- Students who did not complete the homework and failed the test: 4
- Total students who did not complete the homework: \(2 + 4 = 6\)

Now we'll find the total number of students in the class:
\[
\text{Total students} = 21 \, (\text{completed homework}) + 6 \, (\text{did not complete homework}) = 27
\]

Now, we can calculate the probability that a random student from the class completed the homework:
\[
\text{Probability (completed homework)} = \frac{\text{Number of students who completed homework}}{\text{Total number of students}} = \frac{21}{27}
\]

We can simplify this fraction:
\[
\frac{21}{27} = \frac{7}{9}
\]

Thus, the probability that a randomly chosen student completed the homework is \(\frac{7}{9}\).