A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is 

$\frac{24}{25}$

The number of ways in which either player can choose a number from 1 to 25 is 25, so the total number of ways of choosing numbers is 25 × 25 = 625. There are 25 ways in which the numbers chosen by both players is the same.

Therefore, the probability they will win a prize in a single trial is $\frac{25}{625}=\frac{1}{25}$

Hence, the probability that the will not win a prize in a single trial = $1-\frac{1}{25}=\frac{24}{25}$