. You have a bag which contains 100 coins. 99 of these coins are normal and fair having the two sides head and tail. But, one coin is fake and has two heads! You pick a coin randomly out of the bag without checking whether it is a normal coin or the fake one. Suppose that each coin is equally likely to be picked. You throw the picked coin n N times in a row (still without checking whether you have a regular coin or not) and observe the coin lands heads n times. What is the probability that you have picked the fake coin?