Use total and conditional probability for home/away match outcomes.

In any given season, a soccer team plays \(65 \%\) of their games at home. When the team plays at home, they win \(83 \%\) of their games. When they play away from home, they win \(26 \%\) of their games. The team plays one game.

1. Find the probability that the team wins the game.[4]
2. If the team does not win the game, find the probability that the game was played at home.[4]