You are given a bucket that contains 100 coins. 99 of these are fair coins, but one of them is a trick coin that always 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) 0.01.

a. To see if the coin you have is the trick coin, you flip it k times. Let H _k be the event that the coin comes up heads all k If you this occur, what is the conditional probability that you have the trick coin? In Other words, what is P (TlH _k ).

b. HOW many heads in a row would you need to observe in order for conditional probability that have the trick coin to be higher than 99%?