Probability - Waiting-Time and Stopping-Rule Probabilities

Ava and Barry play a game containing one green marble and two red marbles. Each player in turn randomly selects a marble from the bag, notes its colour and replaces it. Ava wins the game if she selects a green marble. Barry wins the game if he selects a red marble. Ava starts the game.

1. Find the probability that Ava wins on her first turn.
2. Find the probability that Barry wins on his first turn.
3. Find the probability that Ava wins in one of her first three turns.
4. Find the probability that Ava eventually wins.