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?

Question

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 \(\frac{7}{9}\).