In a group of 9 people, what is the probability that they all have different birthdays?

Question

[Assume that each is equally likely to be born on any of the 365 days of the year, i.e. no one is born on Feb. 29 in a leap year.]

Answer 1

This is a little strange, either i'm not reading the problem right or the other two answerers are using reasoning I don't understand. Let's get 9 darts, and throw them at a 365 day calendar. The first dart can land on any date. The next one must land on 364 out of the 365 days. The 3rd must land on 363 out of 365, etc, so that the probability is just the product (364)(363)...(357) / 365^8, or about 90.5376%

Answer 2

100% - ((8+7+6+5+4+3+2+1)/365)^2

=99.02720961%


To Princess C: you can't use 9 in the last term because one person of the nine people can only have the same birthday as the remaining *8* people. What you have is the probability for 10 people.

Answer 3

i got almost the same answer.
but here's how i did it:
(1-1/365) (1-2/365) (1-3/365) ... (1-9/365) = .883
then, 1 - .883 = 99.117

Answer 4

i know that it is 50% likely that two ppl will share a birthday when the group is 23 people.