We present three-dimensional numerical simulations of hydrodynamic interaction between a red blood cell (RBC) and a platelet in a wall-bounded shear flow. The dynamics and large deformation of the RBC are fully resolved in the simulations using a front-tracking method. The objective is to quantify the influence of tank treading and tumbling dynamics of the RBC, and the presence of a bounding wall on the deflection of platelet trajectories. We observe two types of interaction: A crossing event in which the platelet comes in close proximity to the RBC, rolls over it, and continues to move in the same direction; and a turning event in which the platelet turns away before coming close to the RBC. The crossing events occur when the initial lateral separation between the cells is above a critical separation, and the turning events occur when it is below the critical separation. The critical lateral separation is found to be higher during the tumbling motion than that during the tank treading. When the RBC is flowing closer to the wall than the platelet, the critical separation increases by several fold, implying the turning events have higher probability to occur than the crossing events. On the contrary, if the platelet is flowing closer to the wall than the RBC, the critical separation decreases by several folds, implying the crossing events are likely to occur. Based on the numerical results, we propose a mechanism of continual platelet drift from the RBC-rich region of the vessel towards the wall by a succession of turning and crossing events. The trajectory deflection in the crossing events is found to depend nonmonotonically on the initial lateral separation, unlike the monotonic trend observed in tracer particle deflection and in deformable sphere-sphere collision. This nonmonotonic trend is shown to be a consequence of the deformation of the RBC caused by the platelet upon collision. An estimation of the platelet diffusion coefficient yields values that are similar to those reported in experiments and computer simulations with multicellular suspension.