If $P ( A \cup B ) = 1 \text { and } P ( A \cap B ) = 0$ , then which statement is true?
A) A and B are complementary events.
B) A and B are supplementary events.
C) A and B are both empty events.
D) A and B are reciprocal events.

Question

Quizplus · Accepted Answer

If $P ( A \cup B ) = 1$ and $P ( A \cap B ) = 0$, then events A and B are mutually exclusive and collectively exhaustive, meaning they cover the entire sample space without overlapping. This makes them complementary events.

If P(A∪B)=1 and P(A∩B)=0P ( A \cup B ) = 1 \text { and } P ( A \cap B ) = 0P(A∪B)=1 and P(A∩B)=0

If $P ( A \cup B ) = 1 \text { and } P ( A \cap B ) = 0$