1.If two events A and B are independent .then

(1). A and complement of B are independent.    

(2). B and complement of A are independent. 

(3). complements of A and complement of B are independent.    ((4) all the above.

2. If two events A and B are independent then

(1) they can be mutually exclusive.   (2)they can not be mutually exclusive.

(3) they can not be exhaustive       (4) both 2 and 3

3. If two events A and B are mutually exclusive then

(1) they are always independent        (2) they may be independent

(3) they can not be independent       (4) they can not be equally likely......

answer with explanations........

1.(4)

2.(4)

3.(3)

I didn't see this question yesterday.

1)A and B are independentP(AB)=P(A)P(B)

P(A'B)=P(B-A)=P(B)-P(B)P(A)=P(A')P(B)

Hence,A',B are independent.similar with B',A.

P(A'B')=1-P(AUB)=1-P(A)-P(B)+P(A)P(B)=(1-P(A))(1-P(B))=P(A')P(B')

Thus,the ans is all the above.

3)I think in the question it must be mentioned that A,B are not impossible events,that is P(A) and P(B) are non zero.If that is the case,then

A,B are mutually exclusiveP(AB)=0P(A).P(B).Hence,they are not independent.