A box contains two coins: a regular coin and one two-headed coin. I choose a coin at random and toss it twice. Define the following events. A = First toss results in a HB = Second toss results in a HC = Regular coin has been selectedAre A and B independent? Are A and B conditionally independent given C? Find P (A|C), P (B|C), P (A∩B|C), P (A), P (B), and P (A∩B), and use them to answer the question.
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