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 completed the homework?

\begin{tabular}{|c|c|c|} \hline & Passed the test & Failed the test \\ \hline Completed the homework & 8 & 4 \\ \hline Did not complete the homework & 2 & 5 \\ \hline \end{tabular}

Solution

To find the probability that a student chosen randomly from the class completed the homework, we follow these steps: First, calculate the total number of students. \[ \begin{aligned} \text{Total students} &= (8 + 4) + (2 + 5) \\ &= 19 \end{aligned} \] Next, calculate the total number of students who completed the homework. \[ \begin{aligned} \text{Completed the homework} &= 8 + 4 \\ &= 12 \end{aligned} \] Finally, find the probability that a randomly chosen student completed the homework by dividing the number of students who completed the homework by the total number of students. \[ \text{Probability} = \frac{12}{19} \]