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 the first song is a rock song and the second is a country song? Write your answer as a fraction in simplest form.
The probability of the first song being a rock song is 2/7, as there are 2 rock songs out of 7 total.
After the first song is played, there are 6 songs remaining, out of which 2 are country songs.
Thus, the probability of the second song being a country song, given that the first is a rock song, is 2/6 or 1/3.
Using the multiplication rule of probability, the probability of both events happening together (first song is a rock song and second is a country song) is:
2/7 * 1/3 = 2/21
Therefore, the probability that the first song is a rock song and the second is a country song is 2/21.