You're a member of the republican party. you go to vote for the party nominee for president. on your ballot are candidates for both the democratic and republican nominations. you're most likely voting in what kind of election?

The superficial answer is that Democrats vote in the Democratic primary, and Republicans vote in the Republican primary. But that's both facetious and fails to address the full complexity of the situation.

There are fifty states, and each state has its own rules for how (and even if) primary elections are conducted in that state. The purpose of a primary is to decide who the party will name, or nominate, as its recommended candidate for some particular office. In a closed primary, only "members" of the party are permitted to vote.