In risky decision-making, expected utility (EU) theory is widely used to examine people's risk attitude and choice behavior. However, it is unknown how risk attitude relates to attention and information search. In this paper, we explore the relationship between risk attitude (as measured by a variant of EU) and eye movement patterns (which serve as a proxy for attention and information search). Participants made choices between gambles presented perceptually as flickering grids in which monetary values were indicated by colors and probabilities by color proportions. To explore attention and information search patterns, we investigated eye movement patterns when faced with different gambles and correlated these patterns with the parameters of EU. We observed that people who are more risk-seeking (as determined by modeling) tend to look at risky options more often. These results bridge choice behaviors conceptualized by EU and information search strategies under risky decision-making revealed by eye movements.