This paper presents a simple parallel algorithm for the Maximal Independent Set (MIS) problem. The first algorithm is a Monte Carlo algorithm with a very local property, where each vertex is randomly chosen to be added to the independent set based only on information about adjacent vertices. This algorithm can be converted into a deterministic algorithm using techniques that reduce the number of random bits required. The resulting deterministic algorithm has the same parallel running time as the Monte Carlo algorithm. The paper also discusses the development of a new probability space with a small sample space where events are pairwise independent, which allows for efficient parallel computation. This technique is used to design a deterministic algorithm for the MIS problem with a running time of O((log n)^2) on a EREW P-RAM, establishing that the MIS problem is in NC^2. The paper also explores applications of the MIS algorithm in various problems, including Maximal Coloring and 2-Satisfiability. It shows that these problems can be reduced to the MIS problem and are thus in NC^2. Additionally, the paper discusses the use of the MIS algorithm in other areas such as artificial intelligence and distributed computing. The paper also addresses open problems in the field, including finding other Monte Carlo algorithms that can be converted into deterministic algorithms and determining the parallel complexity of the MIS problem. It concludes with acknowledgments to those who contributed to the research and references to related works.This paper presents a simple parallel algorithm for the Maximal Independent Set (MIS) problem. The first algorithm is a Monte Carlo algorithm with a very local property, where each vertex is randomly chosen to be added to the independent set based only on information about adjacent vertices. This algorithm can be converted into a deterministic algorithm using techniques that reduce the number of random bits required. The resulting deterministic algorithm has the same parallel running time as the Monte Carlo algorithm. The paper also discusses the development of a new probability space with a small sample space where events are pairwise independent, which allows for efficient parallel computation. This technique is used to design a deterministic algorithm for the MIS problem with a running time of O((log n)^2) on a EREW P-RAM, establishing that the MIS problem is in NC^2. The paper also explores applications of the MIS algorithm in various problems, including Maximal Coloring and 2-Satisfiability. It shows that these problems can be reduced to the MIS problem and are thus in NC^2. Additionally, the paper discusses the use of the MIS algorithm in other areas such as artificial intelligence and distributed computing. The paper also addresses open problems in the field, including finding other Monte Carlo algorithms that can be converted into deterministic algorithms and determining the parallel complexity of the MIS problem. It concludes with acknowledgments to those who contributed to the research and references to related works.