1. **Problem statement:** In a class, 65% of students like green (G), 45% like blue (B), and some like both. We need to find the percentage who like both colors. 2. **Formula used:** For two sets, the percentage liking either or both colors is given by the inclusion-exclusion principle: $$\text{Percentage}(G \cup B) = \text{Percentage}(G) + \text{Percentage}(B) - \text{Percentage}(G \cap B)$$ 3. Since all students like either green or blue or both, the union covers 100% of students: $$100 = 65 + 45 - \text{Percentage}(G \cap B)$$ 4. Solve for the intersection: $$\text{Percentage}(G \cap B) = 65 + 45 - 100 = 110 - 100 = 10$$ 5. **Answer:** 10% of the students like both green and blue colors.