a radio disc jockey has 7 songs on this upcoming hours playlist: 2 are rock songs, 3 are reggae songs, and 2…

a radio disc jockey has 7 songs on this upcoming hours 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.

a radio disc jockey has 7 songs on this upcoming hours 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.

Answer

Explanation:

Step1: Calculate probability of first - rock song

There are 7 songs in total and 2 rock songs. The probability of choosing a rock song first is $\frac{2}{7}$.

Step2: Calculate probability of second - country song

After choosing a rock song first, there are 6 songs left. There are 2 country songs. So the probability of choosing a country song second is $\frac{2}{6}=\frac{1}{3}$.

Step3: Calculate joint probability

Since these are dependent events, we multiply the probabilities of each event. The joint probability is $\frac{2}{7}\times\frac{1}{3}=\frac{2}{21}$.

Answer:

$\frac{2}{21}$