This paper proposes a robot action planning scheme that provides an efficient and probabilistically safe plan for a robot interacting with an unconcerned human -- someone who is either unaware of the robot's presence or unwilling to engage in ensuring safety. The proposed scheme is predictive, meaning that the robot is required to predict human actions over a finite future horizon; such predictions are often inaccurate in real-world scenarios. One possible approach to reduce the uncertainties is to provide the robot with the capability of reasoning about the human's awareness of potential dangers. This paper discusses that by using a binary variable, so-called danger awareness coefficient, it is possible to differentiate between concerned and unconcerned humans, and provides a learning algorithm to determine this coefficient by observing human actions. Moreover, this paper argues how humans rely on predictions of other agents' future actions (including those of robots in human-robot interaction) in their decision-making. It also shows that ignoring this aspect in predicting human's future actions can significantly degrade the efficiency of the interaction, causing agents to deviate from their optimal paths. The proposed robot action planning scheme is verified and validated via extensive simulation and experimental studies on a LoCoBot WidowX-250.