The events A A\,A and B B\,B are such that P(A)=49\displaystyle P(A) = \frac{4}{9}P(A)=94, P(B)=13\displaystyle P(B) = \frac{1}{3}P(B)=31 and P(A∣B)=12\displaystyle P(A|B) = \frac{1}{2}P(A∣B)=21. Find
P(A∩B)P(A \cap B)P(A∩B)
P(B′∣A)P(B'|A)P(B′∣A)
P(A′∪B)P(A' \cup B)P(A′∪B)
Determine whether the events A A\,A and B B\,B are independent, give a reason for your answer.
