Question

Two events A and B will be independent, if (A) A and B are mutually exclusive (B) (C) P(A) = P(B) (D) P(A) + P(B) = 1

Answer 1

Let, A and B be the two events.

Given both A and B are independent,

P( AB )=P( A )⋅P( B )

Now,

P( A ′ B ′ )=[ 1−P( A ) ]⋅[ 1−P( B ) ] P( A ′ ∩ B ′ )=1−P( A )−P( B )+P( A )⋅P( B ) 1−P( A∪B )=1−P( A )−P( B )+P( A )⋅P( B ) P( A∪B )=P( A )+P( B )−P( A )⋅P( B )

Solve further.

P( A )+P( B )−P( AB )=P( A )+P( B )−P( A )⋅P( B ) P( AB )=P( A )⋅P( B )

Hence, the correct option is (B).