Which of the following statements is correct given that the events A and B have nonzero probabilities?
A. A and B are always independent
B. A and B are always mutually exclusive
C. A and B cannot be both independent and mutually exclusive
D. A and B can be both independent and mutually exclusive

Which of the following is a requirement of the probabilities assigned to the outcomes $O_i$:
A. $0 \leq P(O_i)\leq 1$ for each i
B. $P(O_i) = 1 + P(O_i^C)$
C. $P(O_i) \leq 0$
D. $P(O_i) \geq 1$