Obviously, the probability that the first person draws the red ball is m \ n；;
When the second person draws cards, there are two situations:
(1) When the first person draws the red ball, the probability that the second person draws the red ball is
M \ N(M- 1)/(N- 1)= M(M- 1)/[N(N- 1)]
(2) In the case that the first person draws a white ball, the probability that the second person draws a red ball is
(N-M)\ N M/(N- 1)= M(N-M)/[N(N- 1)]
So, the probability that the second person draws the red ball is
M(M- 1)/[N(N- 1)]+M(N-M)/[N(N- 1)]
That is, the second person and the first person have the same probability of winning the red ball, in no particular order.
And so on.