a radio disc jockey has 8 songs on this upcoming hours playlist: 4 are rock songs, 2 are reggae songs, and 2…

a radio disc jockey has 8 songs on this upcoming hours playlist: 4 are rock songs, 2 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 reggae song and the second is a rock song? write your answer as a fraction in simplest form.

a radio disc jockey has 8 songs on this upcoming hours playlist: 4 are rock songs, 2 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 reggae song and the second is a rock song? write your answer as a fraction in simplest form.

Answer

Explanation:

Step1: Calculate the probability of the first song being reggae

The total number of songs is (n = 8), and the number of reggae songs is (m_1=2). The probability of choosing a reggae song first, (P_1=\frac{2}{8}=\frac{1}{4}).

Step2: Calculate the probability of the second song being rock

After choosing a reggae song first, the number of remaining songs is (n_2 = 8 - 1=7), and the number of rock songs is (m_2 = 4). The probability of choosing a rock song second, given that a reggae song was chosen first, (P_2=\frac{4}{7}).

Step3: Calculate the probability of the combined event

For dependent events, the probability (P = P_1\times P_2). Substitute (P_1=\frac{1}{4}) and (P_2=\frac{4}{7}) into the formula: (P=\frac{1}{4}\times\frac{4}{7}=\frac{1\times4}{4\times7}=\frac{1}{7}).

Answer:

(\frac{1}{7})