Let's say a coin is given to you which is shown to have two sides (head and tail). I threw the coin 10 times and I got the sequence HHHHHHHHHH (all heads). Now, I am about to throw it the eleventh time. You lose a large bet if you predict the next toss wrongly. How will you predict the outcome of next toss?
Here are some of my answers:
- It is rare to see 10 heads together unless the coin is biased. Hence, the probability that the coin is biased (the hyperparameter, theta) is very high. So, I should bet that the next outcome will also be a head.
- 10 flips are too small a number to conclude that the coin is biased. Getting 11 heads is extremely rare and hence I must bet on a tail for eleventh toss.
- Coin flips are IID and hence it does not depend on the previous tosses. You can bet on anything and your chances of winning is the same.
Am extremely confused on which of these is a good answer if any of them is a good answer at all. What do you think?