Two events A and B are independent, if
A. A and B are mutually exclusive.
B. $P\left(A' \cap B'\right)=[1-P(A)][1-P(B)]$
C. $P\left(A'\right)=P\left(B'\right)$
D. $P(A)+P(B)=1$
E. $P(A)=P(B)$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → B only
two events are independent if
for A, B $P(A∩B)=P(A)P(B)$
so from (B)
$P(\bar A∩\bar B)=(1-P(A))(1-P(B))$
$=P(\bar A)P(\bar B)$
⇒ testify for independence of A, B