A radio disc jockey has 7 songs on this upcoming hour's playlist: 2 are rock songs, 3 are reggae songs, and 2 are country songs. The disc jockey randomly chooses the first song to play, and then she randomly chooses the second song from the remaining ones. What is the probability that both songs are country songs? Write your answer as a fraction in simplest form.
There are a total of 7 songs, so the probability that the first song chosen is a country song is 2/7. Picking another country song from the remaining 6 songs (since one has already been chosen) gives a probability of 1/6. Therefore, the probability of both songs being country songs is (2/7) x (1/6) = 1/21. So the answer is 1/21.
