This is an interesting topic, and there are a few ways to approach it that come immediately to mind.
Colors in paint and colors in light are somewhat different; paint gains its color from the fact that it reflects some colors and absorbs others, while light simply contains colors. This leads to a few interesting properties, though.
The basics of an experiment might involve shining lights of different colors on pigments or papers of different colors, and testing predictions on what colors will show; you could also shine light through colored filters, which work in essentially the same way. For example, you might predict that a red light shining on white paper would be red, or that a cyan light shining on red pigment would be blue- then, you could test those and find that only one was correct. Using these results, you could make your own theory of how different primary colors make up light and pigments.
You could also take ideas from one of these, as they also involve color composition: [here]
I hope this helped! Feel free to ask more questions if you're not sure about something.