Understanding the influence of users' opinions on their search behavior together with their inherent biases in web search has garnered widespread interest in recent times. This is largely due to the implications of promoting critical thinking, explaining phenomena such as political polarization, or the manifestation of echo chambers. It is important to understand how personal opinions can bias users' interaction with search results. Moreover, there is a lack of understanding of the impact of user search intents, namely non-purposeful browsing versus searching with a pre-defined goal, on users' interactions with search results. We take a step towards bridging this knowledge gap through an empirical study in this paper. To do so, we select two controversial topics in abortion and gun control, and invite users to learn about them through ĝ€ Purposeless' and ĝ€ Purposeful' web searching. Our findings suggest that users with strong personal opinions exhibit biased interactions with the search results. However, the effect of users' opinions on their interactions with search results can differ depending on whether users search purposelessly or with a purpose. Our findings advance the current understanding of the effect of users' opinions in web search sessions, and show that users' search intents shape their interaction with search results. This work has broad design implications on dealing with bias in interactive information retrieval systems.