Question

If two events are independent, then

(A) they must be mutually exclusive

(B) the sum of their probabilities must be equal to 1

(C) (A) and (B) both are correct

(D) None of the above is correct

Answer 1

Answer is (D)

If two events A and B are independent, then we know that

If A and B are independent, knowledge that A occurred does not change the probabilities that B may have occurred. Whereas if A and B are disjoint, knowledge that A occurred completely changes the probabilities that B may have occurred by collapsing it to 0.