Question

A radio disc jockey has 7 songs on this upcoming hour's playlist: 2 are rock songs, 2 are reggae songs, and 3 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.

Answer 1

The answer is 1/7 because you multiply 3/7 x 2/6 and get 1/7.

Answer 2

SAMPLE SPACE ={2 rock, 2 songs, 3 country} = 7 POSSIBLE OUTCOME
1st selection P(country) = 3/7
After the 1st selection, the remaining country =2 and 6 possible outcome,

2nd selection P(also country) = 2/6 = 1/3
Now the condition of selecting 1 country AND 1 country is:

P(country ∩ country) =3/7 x 1/3 = 3/21