Explore randomized complexity theory in this undergraduate lecture focusing on RP, coRP, and ZPP classes. Delve into the concepts of probabilistic Turing machines, randomness, and nondeterminism. Learn about error amplification and randomized polynomial time algorithms. Gain insights into why randomness is important in computational complexity and understand the conditions for these complexity classes. Part of Carnegie Mellon's Computational Complexity Theory course (15-455), this lecture is taught by Ryan O'Donnell and complements Sipser's textbook chapter 10.2.