#### Answer

a)31
b)$\frac{1}{2^{31}}$

#### Work Step by Step

a) Every team will lose exactly once (except the winner), when it gets knocked out, and every atch has one loser, hence there will be 31 losses, hence there will be 31 matches.
b) By the fundamental counting rule there are $2\cdot2\cdot 2\cdot...\cdot2=2^{31}$ possibilities, from which 1 is correct, hence probability=$\frac{1}{2^{31}}$