Probability problems

[kay_wink08]

14. When two teams battle in a championship final, the Stars have a 54% chance of winning a game when playing at home and the Pros have a 57% chance of winning a game when playing at home. In a best-of-three matchup, the first game will be played at the Stars home field, the second game at the Pros home field and the third game back at the Stars home field.
[1] a) What is the probability the Stars win the final in two straight games?
[1] b) What is the probability the Pros win the final in two straight games?
[1] c) What is the probability the Stars win the final in three games?
[1] d) What is the probability the Pros win the final in three games?
[2] e) Create a probability histogram for this distribution.
Pls help!!!!

 

[JeffM]

14. When two teams battle in a championship final, the Stars have a 54% chance of winning a game when playing at home and the Pros have a 57% chance of winning a game when playing at home. In a best-of-three matchup, the first game will be played at the Stars home field, the second game at the Pros home field and the third game back at the Stars home field.
[1] a) What is the probability the Stars win the final in two straight games?
[1] b) What is the probability the Pros win the final in two straight games?
[1] c) What is the probability the Stars win the final in three games?
[1] d) What is the probability the Pros win the final in three games?
[2] e) Create a probability histogram for this distribution.
Pls help!!!!

This is not a brilliantly worded problem, but probably the problem assumes that the result of any one game is independent of the result in another game.

So, question time.
Let a = P(Stars win first game). What is a numerically?
Let b = P(Stars win second game. What is b numerically?
Let c = P(Stars win first and second games). What is c algebraically?

Hints: where do the Stars play the first game?
One rule to MEMORIZE is that P(A + B) = P(A | B) * P(B) if P(B) > 0. And another rule to MEMORIZE is P(A | B) = ??? if A and B are independent?