Could I get some Help with basic probability

1. In a basketball tournament, suppose that the probability that the ‘better’ team wins is 0.6. Given that there are 32 teams and that only the winning team goes through after each game, what is the probability that the best team wins the tournament?

6. Show that P (A ∩ B) − P (A)P (B) = P ((A ∪ B)^c) − P (A^c)P(B^c)

7. Show that if A is independent of itself then either P (A) = 1 or P (A) = 0

Thanks