A box contains three fair coins, and two trick coins that have heads on both sides. (a) What is the probability that a randomly selected coin from the box will come up heads when flipped?   (b) Suppose you randomly pick a coin from the box and flip it, and it comes up heads. What is the probability that it’s one of the trick coins?   (c) Let X be the random variable that represents the number of heads when every coin in the box is flipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes, or you can remember that coin flips are independent of each other.)   (d) What is the expected number of heads when all the coins are flipped? Page 2

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