Standing at the entrance of the building, Annie is going to ask 25 people at random, what day of the year is their birthday. What is the probability that at least two of the 25 were born on the same day of the year? (Neglect leap year considerations, that is if someone says February 29, then Annie does not count that person in recording the 25 birthdays.)
here is what i was thinking
n(S) = 365^25
n(nobody born on the same day) = 365P25
n(somebody born on the same day) = 365^25 - 365P25
P(somebody born on the same day) = (365^25 - 365P25)/365^25
but when I compute this the number I get is .568 which would mean that there is a 56.8% chance that two of the 25 would be born on the same day.
This seems a little high to me, but I guess it could be right...
I was hoping somebody could shed a little light for me, or confirm my results