Probability...

Question

A radio disc jockey has 8 songs on this upcoming hour's playlist: 3 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 both songs are country songs? Write your answer as a fraction in simplest form.

Answer 1

The phrase "from the remaining ones" convinces me that the DJ is not repeating songs during the hour, or at least not immediately, so this is like those problems that read "a bag contains red beans, yellow beans. . ." where one is taken out and not replaced. 

 

We need country, country, so we need the probability that a song is country, which is 2/8.

 

The next time around, there is one fewer country song available and one fewer song total, so second country is 1/7.

 

Multiply together to give joint probability. 

Answer 2

the probability that the first song is a country song is 2 out of 8, which is the same as 1 out of 4  (or 1/4). Now, after picking on of the country songs, the probability that the next song is also a country song is 1/7  (there are seven songs remaining; one of which is a country song, since we assume that you picked one of the country songs already). So, the probability that both songs are country songs is:

 

(1/4)*(1/7)=1/28