If A and B are two mutually exclusive and exhaustive events, then P(B)=1−P(A).
True
Given that, the two events are mutually exclusive and exhaustive.
Mutually exclusive ⇒ P(A ∩ B) = 0
Mutually Exhaustive⇒ P(A ∪ B) = 1
⇒ P(A ∪ B) = P(A) + P(B) − P(A ∩ B) = 1
P(A ∩ B) = 0)
⇒ P(A) + P(B) = 1
⇒ P(B) = 1 − P(A)
Thus, the given statement is true.