Suppose we toss a fair coin, independently, 3 times. Suppose (for our convenience) instead of heads or tails, the sides are marked 1 and 0. If the first coin produced 1, we let X be the maximum of the other two tosses. If the first coin produced 0 we let X be the minimum of the other two tosses. (a) What is the chance that X is 1? Is the event (X = 1) independent of the event that the rst toss produced 1? (b) Do the same problem with a slight change in the definition of X. If the first toss produced 1, we say X is 1 if the other two tosses produce different outcomes and X is 0 otherwise. What is the probability that X = 1? Is the event (X = 1) independent of the event that the first toss produced 1?