1. **State the problem:** We want to determine if event A (student is female) and event B (student prefers romance movies) are independent. 2. **Recall the formula for independence:** Two events A and B are independent if and only if $$P(A \cap B) = P(A) \times P(B)$$ 3. **Calculate probabilities from the table:** - Total students = 200 - Number of females = 90 - Number who prefer romance movies = 80 - Number of females who prefer romance movies = 45 Calculate each probability: $$P(A) = \frac{90}{200} = 0.45$$ $$P(B) = \frac{80}{200} = 0.40$$ $$P(A \cap B) = \frac{45}{200} = 0.225$$ 4. **Calculate $P(A) \times P(B)$:** $$P(A) \times P(B) = 0.45 \times 0.40 = 0.18$$ 5. **Compare $P(A \cap B)$ and $P(A) \times P(B)$:** $$0.225 \neq 0.18$$ Since $$P(A \cap B) \neq P(A) \times P(B)$$, events A and B are **not independent**. 6. **Conclusion:** The event that a student is female and the event that a student prefers romance movies are dependent events. **Final answer:** Event A and event B are not independent.