Every month, the Federal Aviation Administration (FAA) receives over 100 reports of small Unmanned Aircraft Systems (sUAS) operating in airspace where they do not belong and the industry has not deployed any specific, ubiquitous solution to preclude this potential collision hazard for pilots of manned aircraft [1]. The purpose of this research is to determine the key physical attributes and construct a new mathematical model to determine the probability of visual detection and avoidance of sUAS. Using the Monte Carlo simulation method, this study provided a means for addressing the effects of uncertainty in the uncontrollable inputs. As a result, it produced a set of probability curves for various operating scenarios and depicted the likelihood of visually detecting a small, unmanned aircraft in time to avoid colliding with it. This study suggested the probability of detecting a sUAS in time to avoid a collision, in all cases modeled during the study, is far less than 50 percent. The probability was well under 10 percent for sUAS aircraft similar to the products used by many recreational and hobby operators. This study indicated the see-and-avoid is not a reliable technique for collision prevention by manned-aircraft pilots with small, unmanned aircraft and call for regulators and the industry’sdeployment of alternative methods.