Question 376002
The number of ordered pairs (x,y) stemming from A and B choosing one number each is {{{25 * 25 = 25^2}}}.  Of these, there are exactly 25 ordered pairs where the choice of A is the same as the choice of B.  So the probability of winning in a single trial is {{{25/25^2 = 1/25}}}.  Thus the probability of not winning in a single trial is {{{1 - 1/25 = 24/25}}}.