Parents keep telling their teens to “turn down the music” or “turn off the computer” when studying. But teens insist that these “distractions” actually help them study better! In order to put this argument to rest, a psychologist studied whether subjects were able to memorize $20$ index cards while listening to loud music or studying in silence. The sixty subjects had these results:  

1. What is the probability that a randomly chosen subject is able to memorize the index cards?

   Hint (a):

   How many of the subjects were able to memorize the index cards? How many total subjects were there?

2. What is the probability that a music listener memorizes the index cards?

   Answer (b):

   $\frac{9}{45}$

3. According to the data from this study, is the ability to memorize independent of listening to loud music?

   Hint (c):

   If the probabilities from parts (a) and (b) are the same, then the ability to memorize is independent of listening to loud music.