In honor of the March 8 holiday, a competition of performances was organized. Two performances reached the final. \(N\) students of the 5th grade played in the first one and \(n\) students of the 4th grade played in the second one. The performance was attended by \(2n\) mothers of all \(2n\) students. The best performance is chosen by a vote of the mothers. It is known that half of the mothers vote honestly, i.e. for the performance that was truly better and the mothers of the other half in any case vote for the performance in which their child participates.
a) Find the probability of the best performance winning by a majority of votes.
b) The same question but this time more than two performances made it to the final.