N2022 P2 Q6

Amil and Babs are playing a game in which they take turns to throw a fair six-sided die. The winner is the first player to throw the same number as the other player has thrown immediately before. Anil throws first.

1. Find exactly the probability that Anil wins the game.[3]
2. Given that Babs wins the game, find exactly the probability that she wins on her second throw.[3]