One-third of the campers at Rosewood Performing Arts Camp play an instrument. Two-fifths of those campers play the guitar. What fraction of the campers at Rosewood Performing Arts Camp play the guitar?
Let's say there are N campers at Rosewood Performing Arts Camp.
One-third of the campers play an instrument, which is (1/3) * N = N / 3
Two-fifths of those campers play the guitar, which is (2/5) * (N / 3) = (2N) / (5*3) = (2N) / 15
Thus, the fraction of the campers at Rosewood Performing Arts Camp who play the guitar is (2N) / 15. Answer: \boxed{\frac{2}{15}}.
To find the fraction of campers who play the guitar, we first need to find the fraction of campers who play an instrument. Given that one-third of the campers play an instrument, the fraction is 1/3.
Now, we need to find the fraction of those campers who play the guitar. It is stated that two-fifths of the instrument-playing campers play the guitar. Therefore, the fraction of the campers who play the guitar is 2/5.
In conclusion, 2/5 of the campers at Rosewood Performing Arts Camp play the guitar.