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

Question

Quizplus · Accepted Answer

Given that $P(A \cup B) = 1$ implies that together, events A and B cover all possible outcomes, and $P(A \cap B) = 0$ implies that A and B cannot occur at the same time, which means they are complementary events.

If P(A∪B)=1P ( A \cup B ) = 1P(A∪B)=1 And P(A∩B)=0P ( A \cap B ) = 0P(A∩B)=0

If $P ( A \cup B ) = 1$ And $P ( A \cap B ) = 0$