Final answer:
Mitochondria and chloroplasts in eukaryotic cells likely evolved through endosymbiotic events with bacteria. The endosymbiotic theory explains that mitochondria originated from an aerobic bacterium, while chloroplasts originated from a photosynthetic bacterium.
Step-by-step explanation:
The origin of mitochondria and chloroplasts in eukaryotic cells can be explained by the endosymbiotic theory. Mitochondria likely evolved from an ancestral cell engulfing an aerobic bacterium, while chloroplasts originated from the incorporation of a photosynthetic bacterium. This theory is supported by evidence such as shared characteristics between these organelles and prokaryotic cells, as well as the presence of prokaryote-like DNA within mitochondria and chloroplasts.