This lecture introduces randomized algorithms for the min-cut problem, focusing on the Karger's algorithm. The instructor explains the probability of success in finding the minimum cut, the concept of cutting at the right place, and the analysis of different phases of the algorithm. The lecture covers the calculation of probabilities for successful cuts, the importance of edge capacities, and the impact of cutting at the wrong place. Various scenarios and calculations are presented to illustrate the algorithm's efficiency and limitations.