A student with impeccable taste has three genres of music on their smartphone playlist: classical, heavy metal, and new age.

Each genre has a mix of vocal and instrumental tracks. Some of the tracks are good to play while studying, some are good for exercising, and some are good for relaxing. The phone plays tracks at random.

Define events C, H, and N for the three genres of music; V and I for vocal and instrumental music; and S, E, and R for whether the music is suitable for the three different activities.

a. What sample space are we implicitly assuming when we define these events?

b. Based on the context, do you think events C, H, and N are

(i) mutually exclusive, and (ii) independent?

c. Repeat part

(b) for events V and I.

d. Repeat part

(b) again for events S, E, and R.

e. Translate the following statements into probability notation.

i. Probability a track is heavy metal.

ii. Probability a vocal track is classical.

iii. Probability of getting a relaxing, new-age track.

iv. Probability a heavy metal track is good for exercising.

v. Probability a relaxing, instrumental track is heavy metal.

vi. Probability a classical track is good for either studying or relaxing.