As part of a music project for the 2019 Science Fair at SLAS Patiala, 30 horses were made to listen tO Mozart and heavy-metal music. The results were as follows: 

12 of the 30 horses exhibited some head movements when Mozart was played; 

15 exhibited some head movements when the heavy metal was played; and 6 moved their heads when both were played. 

a) If a horse is chosen at random, what is the probability the horse exhibited head movements to Mozart or to heavy metal or to both? 

b) If a horse is chosen at random, what is the probability the horse did not exhibit any head movements to either of the music? 

c) Are the events "Horse moves head when music is played" and "Horse does not move head when the music is played" mutually exclusive and Why?