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

Answer: (B)

$P(A' \cap B') = (1 - P (A)) (1-P(B))$

Answer 2

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 $P(A \cap B)=0$