The events A A\,A and B B\,B are such that P(A)=0.45P(A) = 0.45P(A)=0.45, P(B)=0.6P(B) = 0.6P(B)=0.6 and P(A∣B)=13\displaystyle P(A|B) = \frac{1}{3}P(A∣B)=31.
Find P(A∩B)P(A \cap B)P(A∩B).
Find P(B′∣A)P(B'|A)P(B′∣A).
Find 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.
