this question requires conditional probability
i.e. probability of A = 1 - probability of B
so we have 25 people.
therefore the first persons birthday is 1/365.
the probability that the next person does not have the same birthday is 364/365.
third is 363/365.
fourth is 362/365.
so when we get to the 25th person, the probability that the birthdays are different is:
364/365 * 363/365 * 362/365 * ... * 341/365.
therefore the probability that one person has the same birthday as the other in 1 - this answer.
= 1 - 0.431300296
which is approximately 57%.