What is the probability that of eight randomly selected people, at least two have the same birthday? Assume no leap years. I tried to set this up as a binomial formula problem, with p=(1/365), but I’m sure that can’t be right.
-Ed
The probability is 0.0743353…
You’re welcome.
Thanks. How did you do that?
-Ed
Here are a couple of sites that explain it:
Two People with the Same Birthday
The second one has a nice graph.
With p=1/365 the answer is (7+6+5+4+3+2+1)/365 = 0.076712329
Sailor is way off. By that logic, the same problem with 50 people would have well over 100% probability, clearly wrong.
The correct way is to envision the following:
First phrase the question the opposite way, what are the odds that none share a common birthday?
The first person can have any ol’ day, 365/365.
The second person can have any day but the 1st persons, so 364/365.
The third person can have any day but the 1st and 2nd’s, so 363/365.
and so on.
The answer to that question is (364363362361360359358)/(365^7)
The answer to the OP is that number subtracted from one.
I take that back, … never mind
For n people:
p = 1 - {[364!/(365-n)!]/365^(n-1)}
I mean it. You’re welcome. Really.