Historically, two rival teams have been closely matched, and during a regular season, they play each other
twice. The probability that Team A wins the first game is 0.45. If Team A wins the first game, the probability
that they also win the second game is 0.30. If they lose the first game, the probability that Team A wins the
second game is 0.65. For parts (a-d), do not round your answers. For part (e) round your answer to three
decimal places. (11 pts)
a) Create a tree diagram for the scenario above.
b) What is the probability that Team A wins both games?
c) What is the probability that Team A wins exactly one game?
d) What is the probability that Team A wins the second game?
e) Given Team A wins the second, what is the probability they won the first game?