1. **State the problem:** We have a class with students categorized by whether they completed homework and whether they passed the test. We want to find the probability that a student who did not complete the homework passed the test. 2. **Identify the relevant data:** From the table: - Students who did not complete homework and passed the test: 2 - Students who did not complete homework and failed the test: 6 3. **Recall the formula for conditional probability:** $$P(\text{Passed} \mid \text{Did not complete homework}) = \frac{\text{Number who passed and did not complete homework}}{\text{Total number who did not complete homework}}$$ 4. **Calculate the total number of students who did not complete homework:** $$2 + 6 = 8$$ 5. **Calculate the probability:** $$P = \frac{2}{8}$$ 6. **Simplify the fraction:** $$P = \frac{\cancel{2}}{\cancel{8}} = \frac{1}{4}$$ 7. **Interpretation:** The probability that a student who did not complete the homework passed the test is $\frac{1}{4}$ or 0.25.