Consider two players P1 and P2:
- P1 has one fair coin.
- P2 has two coins. One of them is fair, whereas the other one is 2-headed (Her Majesty is on both sides of this coin).
The two players P1 and P2 play a game in which they alternate making turns: P1 starts, after which it is P2's turn, after which it is P1's turn, after which it is P2's turn, etc.
- When it is P1's turn, she flips her coin once.
When it is P2's turn, he does the following:
- P2 chooses one of his two coins uniformly at random. Then he flips the chosen coin once.
- If the first flip did not results in heads, then P2 repeats this process one more time: P2 again chooses one of his two coins uniformly at random and flips the chosen coin once
The player who flips heads first is the winner of the game.
- Determine the probability that P2 wins this game, assuming that all random choices and coin flips made are mutually independent. Justify your answer.
Just need a little help figuring out the answer.
I get that when it is P2's turn he has two chances of getting heads, and if he gets the 2-headed coin he wins and if he gets the fair coin he has a 50-50 chance of getting heads.
But what I can't figure out is how to actually calculate his probability of winning.