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?

Question

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).