Imagine you roll 2 fair 6-sided dice.
(a) Let C denote the event that the sum of the dice is 3. Let B denote the event that the first die is a 1. Show that C and B either are or are not independent. Intuitively, why does your conclusion make sense?
(b) Let A denote the event that the sum of the dice is 7. Show that A and B either are or are not independent. Does your conclusion match your intuition?