3. Suppose a hand of 5 cards is dealt from a shuffled standard deck of 52 cards. Consider the following events P (A ) A: "the hand contains no club"; B: "the hand contains no face card": PCA) = 1 i P ( B ) = 1 C: "the hand contains no red card". 13 12 1 PCC ) = 1 26 PCA) = 1 = 36 P(B)= 1-1265 , P (() = 1- 26 26 (a) Calculate P(A|B) and P(A C). P(AIB ) = P(AnB ) PCB ) 0: 999 (b) Are the events A and B independent? Why or why not? yes PCA ) - 8 (c) Are the events A and C independent? Why or why not? Yes