Question

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.

Answer 1

Answer:

Step-by-step explanation:

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 .