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Let a be the event that the number of heads is even does

Question: Let (S₃, Prob) be the probability space of the experiment of flipping three coins.

(i) Let A be the event that the number of heads is even. Does there exist an event B ⊂ S₃ such that A and B are independent?

(ii) Let D be the event that either the result of the second coin flipping is tail or the result of the third coin flipping is tail. Find all events C such that C and D are independent.

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Basic Statistics: Let a be the event that the number of heads is even does

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