State with evidence, whether each of the following statements is true or false:

a. If events A and B are mutually exclusive, the conditional probability of A, given B, is equal to the probability that event A occurs times the probability that event B occurs.

b. If events A and B are independent, the conditional probability of A given B is equal to the probability that event A occurs times the probability that event B occurs,

c. The conditional probability of A given B is equal to the probability of event A if events A and B are independent.

d. When two events are independent, the probability of both occurring is the sum of the probabilities of the individual events.