The lottery paradox is considered to be one of the biggest problems concerning fallibilism in epistemology. This paper offers a presentation and critical analysis of two different contextualistic solutions to that paradox. The first part of the paper deals with the lottery paradox and Stewart Cohen’s proposed solution. The second part is a presentation of David Lewis’ solution to that epistemological problem. The two analyses offered serve to show that Cohen is (while Lewis is not) committed to the claim that the same solution can be used for both: the lottery paradox and for the problem of skepticism. In the final part of the paper the main focus is on the question whether the same explanation of how conversational mechanisms work can really serve to explain these two problems of contemporary epistemology. It is argued, mainly on the basis of modal interpretation of the relevant alternatives approach, that there is a significant difference in structure between these two problems, and that they, therefore, deserve different treatment.