Answered

In a class of students, the following data table summarizes how many students passed a test and completed 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?

\begin{tabular}{|c|c|c|}
\hline
& Passed the test & Failed the test \\
\hline
Completed the homework & 12 & 6 \\
\hline
Did not complete the homework & 3 & 4 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let's determine the probability that a randomly chosen student from the class either passed the test or completed the homework. We will proceed step-by-step:

1. Identify and sum up the total number of students:
- Students who passed the test and completed the homework: 12
- Students who failed the test and completed the homework: 6
- Students who passed the test and did not complete the homework: 3
- Students who failed the test and did not complete the homework: 4

Total number of students = [tex]\(12 + 6 + 3 + 4 = 25\)[/tex]

2. Identify the number of students who passed the test:
- Students who passed the test and completed the homework: 12
- Students who passed the test and did not complete the homework: 3

Number of students who passed the test = [tex]\(12 + 3 = 15\)[/tex]

3. Identify the number of students who completed the homework:
- Students who passed the test and completed the homework: 12
- Students who failed the test and completed the homework: 6

Number of students who completed the homework = [tex]\(12 + 6 = 18\)[/tex]

4. Determine the number of students who either passed the test or completed the homework:
Using the principle of inclusion and exclusion:
[tex]\[ \text{Number of students who either passed or completed} = (\text{Number who passed}) + (\text{Number who completed}) - (\text{Number who did both}) \][/tex]
Number of students who did both (passed the test and completed the homework): 12

[tex]\[ \text{Number who either passed or completed} = 15 + 18 - 12 = 21 \][/tex]

5. Calculate the probability:
Probability of choosing a student who either passed the test or completed the homework:
[tex]\[ \text{Probability} = \frac{\text{Number who either passed or completed}}{\text{Total number of students}} = \frac{21}{25} \][/tex]

Simplifying the fraction if necessary:
[tex]\[ \frac{21}{25} = 0.84 \][/tex]

So, the probability that a randomly chosen student from the class either passed the test or completed the homework is [tex]\( \frac{21}{25} \)[/tex] or 0.84.