Modern vehicles increasingly rely on advanced driver-assistance systems (ADAS), with radars playing a key role due to their cost-effectiveness and reliable performance. However, the growing number of radars operating in the same spectrum raises concerns about mutual interference, which could lead to system malfunctions and potential safety risks. This study focuses on a scenario in which all vehicles are equipped with frequency-modulated continuous-wave (FMCW) radars, and it assesses the impact of interference on radar functionality - expressed in terms of probability of failure - by considering both direct and reflected signals. The radars may employ one of the following proactive mitigation methods to reduce the impact of interference, all of which require no inter-vehicle coordination but differ in complexity: (i) random carrier-frequency hopping on a frame-by-frame basis, (ii) random carrier-frequency hopping on a chirp-by-chirp basis, and (iii) a directional, compass-based method specifically addressing interference from opposite directions, which can be combined with either of the two previous methods. In this work, we assume realistic simulated road traffic scenarios and develop a novel model that captures correlated interference and accounts for the main radar setting parameters. Results reveal that dense scenarios pose a high risk of radar malfunctions. Among the analyzed methods, chirp-by-chirp frequency hopping emerges as the most effective approach to mitigate interference and ensure system reliability, but only when combined with a sufficiently large bandwidth. The compass-based method, on the other hand, shows limited effectiveness and appears not worth the additional system complexity.

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