Let A, B and C be three events such that P(C)=0
Statement-1: $(A ∩ B ∩ C) = 0$
Statement-2:$(A ∩ B ∩ C) = P(A ∪ B)$
Answer & explanation
Correct answer: option 2
We know that
$A ∩ B ∩ C ⊆ C$
$∴ P(A ∩ B ∩ C) ≤ P(C)=0 ⇒ P(A ∩ B ∩ C) =0$
So, statement-1 is true.
Similarly, $ A ∩ C ⊆ C$ and $ B ∩ C ⊆ C$
$⇒ P(A ∩ C) =0 $ and $P(B ∩ C)=0$
$∴ P(A ∪ B∪C)=P(A) +P(B) +P(C) -P(A ∩B) -P(B ∩ C) -P ( C∩A)+P(A ∩ B ∩ C)$
$⇒P(A ∪ B∪C)=P(A) +P(B) +0 - P(A ∩ B) -0-0 +0$
$⇒P(A ∪ B∪C)=P(A) +P(B) +P(A ∩ B) = P(A ∩ B)$
So, statement-2 is true.