Question

Two events $A$ and $B$ will be independent if

• A. A and B are mutually exclusive
• B. $P(A' \cap B') = (1 - P (A)) (1-P(B))$
• C. $P (A) = P(B) $
• D. $ P (A) + P(B) = 1 $

Answer 1

The Correct Option is B

If $A$ and $B$ are two independent events, then $P(A \cap B)=P(A) \cdot P(B)$ Also, if $A$ and $B$ are independent then A' and B' are also independent. $ \therefore P\left(A' \cap B'\right) =P\left(A'\right) \cdot P\left(B'\right)$ $=(1-P(A))(1-P(B)) $ Again, if $A$ and $B$ are mutually exclusive, then $P(A \cap B)=0$