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In the last few years, Unmanned Aerial Vehicles (UAVs) are making a revolution as an emerging technology with many different applications in the military, civilian, and commercial fields. The advent of autonomous drones has initiated serious challenges, including how to maintain their safe operation during their missions. The safe operation of UAVs remains an open and sensitive issue, since any unexpected behavior of the drone or any hazard would lead to potential risks that might be very severe. The motivation behind this work is to propose a methodology for the safety assurance of drones over the Internet (Internet of drones (IoD)). Two approaches will be used in performing the safety analysis: (1) a qualitative safety analysis approach, and (2) a quantitative safety analysis approach. The first approach uses the international safety standards, namely ISO 12100 and ISO 13849 to assess the safety of drone's missions by focusing on qualitative assessment techniques. The methodology starts from hazard identification, risk assessment, risk mitigation, and finally draws the safety recommendations associated with a drone delivery use case. The second approach presents a method for the quantitative safety assessment using Bayesian Networks (BN) for probabilistic modeling. BN utilizes the information provided by the first approach to model the safety risks related to UAVs' flights. An illustrative UAV crash scenario is presented as a case study, followed by a scenario analysis, to demonstrate the applicability of the proposed approach. These two analyses, qualitative and quantitative, enable all involved stakeholders to detect, explore and address the risks of UAV flights, which will help the industry to better manage the safety concerns of UAVs.