The electrical distribution system is moving toward a more decentralized, complex, and dynamic system. The system is experiencing a higher penetration of distributed energy resources, flexible resources, and active end-users, leading to an active distribution system. If these components are used actively, they can have a positive effect on the distribution system's reliability. This paper aims to investigate how a microgrid with renewable energy sources and energy storage might influence the reliability of electricity supply in a radially operated distribution system. The reliability is investigated from both the distribution system perspective and the microgrid perspective with the application of different scenarios. A reliability assessment method for modern distribution systems based on Monte Carlo simulations is presented. The method includes load flow calculations to capture the behavior of the system and system components. The model is tested on the IEEE 33-bus network. The result is confirmed through statistical testing showing the statistical significance in providing support from the microgrid on the distribution system's reliability.