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 failed the test?
Passed the test Failed the test
Completed the homework 11 4
Did not complete the homework 2 5
Answer

Answer 1

To find the probability that a randomly chosen student failed the test, we first need to determine the total number of students and how many of them failed the test.

From the data given:

- Students who **passed the test** and **completed the homework**: 11
- Students who **failed the test** and **completed the homework**: 4
- Students who **passed the test** and **did not complete the homework**: 2
- Students who **failed the test** and **did not complete the homework**: 5

Now, let's calculate the totals:

1. **Total number of students** who **passed the test**:
- 11 (completed homework) + 2 (did not complete homework) = 13

2. **Total number of students** who **failed the test**:
- 4 (completed homework) + 5 (did not complete homework) = 9

3. **Total number of students in the class**:
- Total = Passed + Failed = 13 (passed) + 9 (failed) = 22

Now we can calculate the probability that a randomly chosen student failed the test. The probability \( P \) that a student failed the test is given by the formula:

\[
P(\text{failed}) = \frac{\text{Number of students who failed}}{\text{Total number of students}} = \frac{9}{22}
\]

Thus, the probability that a randomly chosen student failed the test is:

\[
\frac{9}{22}
\] (or approximately 0.4091, if needed in decimal form).