Can two events with nonzero probabilities be both independent and mutually exclusive? Choose the correct answer below. A. Yes,
two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities add up to one. B. No, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero. C. Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities are equal. D. No, two events with nonzero probabilities cannot be independent and mutually exclusive because independence is the complement of being mutually exclusive.
B. No, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero.
For two mutually exclusive events , with non- zero probabilities , when one occurs , the other can not happen . In this way they become dependent events . In this way , for two events to be both independent and mutually exclusive , at least one of the two events must have zero probability .
