A and B play a game where each is asked to select a number from 1 to 25. If the numbers selected by A and B match, both of them win a prize. The probability that they win their third prize on 5^th game is equal to

$\frac{6 .(24)^2}{(25)^5}$

Probability of winning the prize in single game

$=\frac{25}{25^2}=\frac{1}{25}$

In this case first 4 games, must result in exactly two prizes and 5th game must result in prize.

Thus, required probability

$={ }^4 C_2\left(\frac{1}{25}\right)^2 . \left(\frac{24}{25}\right)^2 . \frac{1}{25}$

$=\frac{6.24^2}{(25)^5}$