Engineering decisions that have the greatest effect on worker and public safety occur early in the design process. During these decisions, engineers rely on their experience and intuition to estimate the severity and likelihood of undesired future events like failures, equipment damage, injuries, or environmental harm. These initial estimates can then form the basis of investment of limited project resources in mitigating those risks. Behavioral economics suggests that most people make significant and predictable errors when considering high consequence, low probability events. These biases have not previously been studied quantitatively in the context of engineering decisions, however. This paper describes preliminary results from a set of computerized experiments with engineering students estimating, prioritizing, and making design decisions related to risk. The undergraduate students included in this experiment were more likely to underestimate than overestimate the risk of failure. They were also more optimistic of the effects of efforts to mitigate risk than the evidence suggested. These results suggest that considerably more effort is needed to understand the characteristics and qualities of these biases in risk estimation, and understand what kinds of intervention might best ameliorate these biases and enable engineers to more effectively identify and manage the risks of technology.