Scenario: The following teams are paired up. Just as with the 2007 Division Series, each pair will play a "best 3-out-of-5" series.

• Team A vs. Team B: in each game Team A has a 0.58 probability of winning
• Team C vs. Team D: in each game Team C has a 0.57 probability of winning
• Team E vs. Team F: in each game Team E has a 0.51 probability of winning
• Team G vs. Team H: in each game Team G has a 0.56 probability of winning

Using the information above, answer the following questions. (Note: When calculating your answers, it is important not to round intermediate values too much or your final answers will be incorrect. For best results don't round any numbers to less than 6 decimal places.)

(a) What is the probability that Team A beats Team B in a 3-game sweep (i.e. wins 3 in a row without a loss)? What is the probability that Team B beats Team A in a 3-game sweep? What is the probability that the playoff series between Teams A and B results in a 3-game sweep? (b) What is the probability that the playoff series between Teams C and D results in a 3-game sweep? (c) What is the probability that all 4 of the playoff series (A vs. B, C vs. D, E vs. F, and G vs. H) all result in a 3-game sweep?