Question

PLEASE HELP 20 POINTS!

A radio disc jockey has 8 songs on this upcoming hours playlist: 2 are rock songs, 3 are reggae songs, and 3 are country songs. The disc jockey randomly chooses the first song to play, and then she randomly choses the second song from the remaining ones. What is the probability that BOTH songs are reggae songs? Write your answer as a fraction in the simplest form.

Answer 1

The probability of choosing a reggae song as the first song is 3/8, since there are 3 reggae songs out of a total of 8 songs.

After playing the first song, there are 7 songs left, out of which 2 are rock songs, 2 are reggae songs, and 3 are country songs.

So, the probability of choosing a reggae song as the second song, given that the first song was a reggae song, is 2/7, since there are 2 reggae songs left out of a total of 7 songs.

To find the probability that BOTH songs are reggae songs, we multiply the probability of choosing a reggae song as the first song by the probability of choosing a reggae song as the second song, given that the first song was a reggae song:

(3/8) x (2/7) = 6/56 = 3/28

Therefore, the probability that BOTH songs are reggae songs is 3/28.