Question: In a class of students, the following data table summarizes how many students passed a test and…

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?

Solution

To find the probability that a student chosen randomly from the class failed the test and did not complete the homework, we need to use the table provided. First, identify the number of students who failed the test and did not complete the homework. From the table, this is 6. Next, find the total number of students in the class. Sum all the values in the table: \[ \begin{aligned} & \text{Passed and completed homework} = 9 \\ & \text{Failed and completed homework} = 2 \\ & \text{Passed and did not complete homework} = 3 \\ & \text{Failed and did not complete homework} = 6 \\ \end{aligned} \] Calculate the total: \[ 9 + 2 + 3 + 6 = 20 \] Now, calculate the probability: \[ \text{Probability} = \frac{\text{Number of students who failed and did not complete homework}}{\text{Total number of students}} = \frac{6}{20} \] Simplify the fraction: \[ \frac{6}{20} = \frac{3}{10} \] Therefore, the probability that a student chosen randomly from the class failed the test and did not complete the homework is \(\frac{3}{10}\).