In this chapter, we learn some basic randomized algorithmsand their analyses. Randomized algorithms are a type of probabilistic algorithm. In some contexts, the term probabilistic algorithms may be used in two different meanings: The algorithm itself uses random bits or probabilistic data is input to some deterministic algorithms. In general, when we refer to randomized algorithms, we mean that we are considering the algorithms on a computational model that has some access to random bits. There is a random machine model that assumes that it can obtain one random bit of 0 or 1 uniformly at random in one step and another random machine model that can obtain one random real integer number in some range uniformly at random in one step. Using this feature neatly, we can design simple and powerful algorithms. In this chapter, we will touch on some of their charm.