Question

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

Answer 1

there are 8 songs total...thats what you look at first....now you look at the breakdown of that 8....4 are rock...2 are reggae and 2 are country...

so 4/8 = rock
2/8 = reggae
2/8 = country

the probability it chooses rock is the first time is 4/8

now for the second one, it's different....the song choices go down by 1....so now there are only 7 choices....so now the probability is 3/7 that the second choice is rock.

So you add those 2 fractions

4/8 + 3/7

find common denominator

28/56 + 24/56

now add

52/56

simplify

13/14