4. (5 points) Suppose that you have two coins, one biased and one fair. Coin 1 is biased and comes up tails with probability 7/9, while coin 2 is fair and will flip tails with probability 1/2. Suppose that you pick a coin at random and flip it. Let C; denote the event that coin i is picked for i = 1, 2. Let H and T denote the possible outcomes of the flip. 1) (1 point) Draw a tree diagram for this sequential experiment. 2) (2 points) Given that the outcome of the flip is a head, what is P(C, | H), the probability that you picked the biased coin? 3) (2 points) Given that the outcome is a tail, what is the probability P(C, | T), that you picked the biased coin