Which of the following statements is correct if the events A and B have nonzero probabilities?
A)A and B cannot be both independent and disjoint
B)A and B can be both independent and disjoint
C)A and B are always independent
D)A and B are always disjoint

Question

Quizplus · Accepted Answer

If A and B are disjoint (meaning they cannot both happen at the same time), then knowing that A occurs tells us that B cannot occur, which violates the definition of independence (where the occurrence of one event does not affect the probability of the other). Therefore, A and B cannot be both independent and disjoint if they have nonzero probabilities.

Which of the Following Statements Is Correct If the Events