Final answer:
Luria and Delbrück's experiments supported the mutation theory within Darwin's framework of evolution, demonstrating that mutations occur randomly, which are then acted upon by natural selection.
Step-by-step explanation:
Luria and Delbrück's experiments with bacteria helped to prove the mutation theory supported by Charles Darwin. Their work demonstrated that genetic mutations occur in bacteria at random, prior to exposure to an antibiotic, thus providing evidence for the role of random mutation in evolution and natural selection, as described by Darwin. This contradicted the theory of acquired characteristics proposed by Lamarck and supported the idea that advantageous genetic mutations can give rise to traits that are selected for over time, contributing to the evolution of species.