25. On a circle, there are $n \geqslant 3$ points. A pair of them is chosen at random. Find the probability that the chosen points were "neighbors".
Solution. Elementary outcomes - pairs of numbers $(m, k), m \neq k$, $1 \leqslant m, k \leqslant n$. The total number of elementary outcomes is $(n)_2$, suitable ones are $-n \cdot 2$ (the first point is chosen arbitrarily, then there are only two options for the second). The desired probability is $P_{n}=2 n /(n)_2=2 /(n-1)$.