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:

24/25

P(winning prize) ⇒ both choose same no.

Let 'A' start the game. 'A' can choose anything. 'B' must choose that no.

⇒ P(winning prize) = P(A choose) × P(B/A has choosen) = $1×\frac{1}{25}=\frac{1}{25}$

⇒ P(loosing prize) = $1 - \frac{1}{25}=\frac{24}{25}$