Question

Let A and B be two events such that `P(A cup B)=P(A cap B)`. Then,
Statement-1: `P(A cap overline(B))=P(overline(A) cap B)=0`
Statement-2: `P(A)+P(B)=1
A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer 1

Correct Answer - C
we have,
` P ( cup B) = P ( A cap B)`
` Rightarrow P ( A) + P (B) -P ( A cap B) = P ( A cap B)`
` Rightarrow (P (A) -P ( A cap B) = P ( A cap B) } + { P (B) - P (A cap B)} =0`
` Rightarrow P ( A cap overlineB) + P ( overlineA cap B) =0`
` Rightarrow P ( Acap overline B) = P ( overline A cap B) =0`
So, statement -1 is true.
From (i), we have
` P (A)n + P(B) = 2P ( A cap B)`
So , P (A) + P(B) =1 may not be true.