The events A A\,A and B B\,B are such that P(A)=516\displaystyle P(A) = \frac{5}{16}P(A)=165, P(B)=12\displaystyle P(B) = \frac{1}{2}P(B)=21 and P(A∣B)=14\displaystyle P(A|B) = \frac{1}{4}P(A∣B)=41.
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.
