Suppose you roll a fair sided die (in the shape of a cube, with sides having numbers 1, 2, 3, 4, 5, 6 on them, as usual] and a fair 4sided die (in the shape of a regular tetrahedron, with sides having numbers 1, 2, 3, 4 on them}. Let A be the event that you roll a 1, 2, or 3 on the Eisided die, and let B be the event that you roll a 1 or 2 on the 4sided die. Let C be the event that you roll a 1 or 2 on the sided die and a 1 on the clsided die OR. you roll at least 4 on the sided die and at least 3 on the 4sided die. (a) (4 points) Are A, B, and C independent? (Use the denition in the box on p. 5?. Read the note below the box that explains that you need to verif}r 3 equations to prove independence of 3 events. However, if an},r of these equations fail to hold, then you can conclude that A, B, and C are not independent, and you don't need to check an},r Inore equations.) (b) (2 points) Are A and B independent? (e) (2 points) Are B and C independent? ([1) (2 points) Are A and C independent