First, this is "sampling without replacement" (he can't choose the same person twice) so the events are NOT "independent". The probability he chooses two girls is equal to the probability the first student chosen is a girl multiplied by the probability the second student is a girl given that the first student chosen was a girl.
Initially, there are 25 students, 10 of whom are girls. Assuming all students are equally likely to be chosen, what is the probability that the first student chosen? Now how many students are left to choose from? How many of them are girls?