For events A and B we have

P(A) =0.3 P(B) = 0.8 P(A∪B) = 0.9

a) Find P(A|B) P(A'∩B) P(B'∪A').

b) Are A and B independent? Why?

Any help would be appreciated.

Here is my response that i tried... Am not sure if its correct

part a)

P(A|B) = (P(A)P(B))/P(B)

=0.3

P(A') 1-P(A) =0.7

P(B') 1-P(B) = 0.2

P(A'∩B) = P(A')P(B)=0.56

P(B'∪A') = P(A')+P(B')=0.9

part b)

Case 1

P(A∩B) = P(A)P(B)=.24

P(A|B) = P(A∩B)/P(B) =rearrange and find P(A∩B) = 0.24

Case 2

P(B|A) = P(B)=0.8

P(B|A) = P(B∩A)/P(A) = (P(B)P(A))/P(A) =.8

Since Case 1&2 are both true A&B are independent.