Team A and Team B will be playing each other in a sporting event where there is one winner and one loser; a tie is impossible. A man, wanting to make money from placing a bet on the winner, consults with three omniscient seers. These seers know the outcome of the game already, being omniscient.
The first seer informs the man (truthfully) that he randomly lies 20% of the time when telling the outcome of a sporting event, telling the truth the rest of the time.
The second seer says (truthfully) that he is just like the first, except he lies 40% of the time.
The third seer says (truthfully) that he is just like the first and second seers, except he lies 70% of the time.
The first seer tells the man that team A will win. The second seer tells the man that team A will lose. The third seer tells the man that team A will win.
What is the probability that team A will win?
Each seers' determination of whether to lie is independent of the others. You can imagine that each seer rolls a ten sided die to make their decision of whether to lie.
After the above question is answered, I am curious if someone can come up with a general formula for any number of seers with any probability of lying, with any set of predictions.