The events C C\,C and D D\,D are such that P(C)=25\displaystyle P(C) = \frac{2}{5}P(C)=52, P(D)=34\displaystyle P(D) = \frac{3}{4}P(D)=43 and P(C∣D)=13\displaystyle P(C|D) = \frac{1}{3}P(C∣D)=31.
Find P(C∩D)P(C \cap D)P(C∩D).
Find P(D′∣C)P(D'|C)P(D′∣C).
Find P(C′∪D)P(C' \cup D)P(C′∪D).
Determine whether the events C C\,C and D D\,D are independent, give a reason for your answer.
