Modern Graphics Processing Units (GPUs) have dedicated hardware to execute floating-point operations with different precisions (64-bit double, 32-bit single, and 16-bit half). Using reduced precision for specific applications like Deep Neural Networks (DNNs) has been shown to reduce both the execution time and power consumption with negligible effects on the DNNs' accuracy. As GPUs are playing a critical role in DNN for object detection and get into safety-critical environments, their reliability is becoming a growing concern. In this paper, we evaluate the reliability of a DNN implemented in three different precisions (half, single, and double) on NVIDIA mixed-precision GPUs. We evaluate not only the error rate of the applications but also the effects of the errors on the final detection. We perform extensive fault-injection campaign on the register file of NVIDIA mixed-precision GPUs. We found that reducing data and operation precision increases the probability for the fault to impact the DNN detection and classification. Then, we complement the fault injection study with beam experiments. We exposed YOLOv3 running on Tesla V100s to neutron beams and found that the use of half precision reduces the error rate of up to 2x. The smaller exposed area and improved performances brought by reduced precision is then likely to increase the DNN reliability.