In the final of a contest of performances on March 8 two performances were left. In the first, \(n\) pupils from the class 5A performed, and in the second – \(n\) pupils of class 5B. At the play there were \(2n\) mothers of all \(2n\) students. The best performance is chosen by a vote by the mums. It is known that every mother, with a probability of \(\frac 12\), votes for the best performance and with a probability of \(\frac 12\) – for the performance in which her child participates.
a) Find the probability that the best performance will win with a majority of votes.
b) The same question, if more than two classes have reached the finals.