818 Facebook Friends, 0 Birthdays

[kmac1112]

Hi all, first time poster here. I am an avid facebooker and like to wish people happy birthdays when they come up. Today, for the first time, I noticed that 0 birthdays fell on this particular day.

This got me thinking about what the statistical probability of this happening is...818 friends, 365 days in a year, and 0 birthdays. It's been a while for me since my last Stats class, so I was hoping someone could help me out!

Thanks,

Kevin

[Mean Joe]

2 months ago similar question

An answer is (1 - 1/365.25)^818

[kmac1112]

Hi Mean Joe, is this the same as (364/365)^818?

[KLaw Squared]

I've also noticed that when I increase the value of friends from 818 to a higher #, the % decreases with your formula. This doesn't seem right.

I can't seem to figure this one out either.

[hlsmith]

I don't think you are performing the calculations in the right order, it works for me.

1/365.25 = 0.0027378508
1 - 0.0027378508 = 0.9972621492
0.9972621492^818 = 0.1061785301, seems correct.
Substitute 900 for 818 and got 0.0847898311, seems correct.

[KLaw Squared]

Okay, I think I've got it. The end result is the % odds that no one has a birthday on that date, meaning the higher the sample, the lower the %. Thanks.

[hlsmith]

364/365 = 1-(1/365), so yes, but when you add the 0.25 slight discrepancies emerge between the numbers.