In order to address privacy concerns, many social media websites allow users to hide their personal profiles from the public. In this work, we show how an adversary can exploit an online social network with a mixture of public and private user profiles to predict the private attributes of users. We map this problem to a relational classification problem and we propose practical models that use friendship and group membership information (which is often not hidden) to infer sensitive attributes. The key novel idea is that in addition to friendship links, groups can be carriers of significant information. We show that on several well-known social media sites, we can easily and accurately recover the information of private-profile users. To the best of our knowledge, this is the first work that uses link-based and group-based classification to study privacy implications in social networks with mixed public and private user profiles.