1. **State the problem:** We have a class of 31 students. Some revised and some did not. Among those who revised, 11 passed and 7 did not pass. Among those who did not revise, 5 passed and 8 did not pass. 2. **What is asked?** Given that a student did not pass, find the probability that the student revised. 3. **Recall the formula for conditional probability:** $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$ where $A$ is the event "student revised" and $B$ is the event "student did not pass". 4. **Identify the numbers:** - Number of students who did not pass and revised: 7 - Number of students who did not pass and did not revise: 8 - Total number of students who did not pass: $7 + 8 = 15$ 5. **Calculate the probability:** $$P(\text{revised} | \text{did not pass}) = \frac{7}{15}$$ 6. **Final answer:** The probability that a student revised given they did not pass is $\boxed{\frac{7}{15}}$.