You are given a bucket that contains 1000 coins. 999 of these are fair coins, but one of them is a trick coin that always comes up heads. You select one coin from this bucket at random. Let T be the event that you select the trick coin. This means that P(T) = 0.001. a. Suppose you flip the coin k times. Let Hk be the event that the coin comes up heads all k times. If you see this occur, what is the conditional probability that you have the trick coin? In other words, what is P(T|HR). b. How many heads in a row would you need to observe in order for the conditional probability that you have the trick coin to be higher than 99%?