I have a bag of 10 coins; 1 of them has heads on both sides, while the rest are normal (have heads on one side and tails on the other). Each face of a coin is equally probable when tossed. You choose 1 of the coins from the bag at random and then flip it 100 times observing heads every time. What is the probability that you chose a normal coin?
The probability that we take a normal coin is 9/10 and in 100 turns, it may be (9/10)^100, but I am not sure if this is correct.