Exercise 5
A fair 6-sided die is rolled once.
The sample space is $S = \{1, 2, 3, 4, 5, 6\}$.
Consider the events $A = \{1, 3, 5\}$, $B = \{2, 4\}$
and $C = \{1, 2, 5, 6\}$.
(a) Are A and C independent? Compare $P(C)$ and $P(C|A)$
(b) Are B and C independent? Compare $P(C)$ and $P(C|B)$
(c) Are C and C' independent?