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September 12th, 2019, 12:36 AM  #1 
Newbie Joined: Sep 2019 From: Washington State, USA Posts: 1 Thanks: 0  Family birthday probability
What are the chances that a family of four all have their birthdays land on the same day of the week every year? Just curious if it's as odd as it seems.
Last edited by hendersonrobyn; September 12th, 2019 at 12:38 AM. 
September 12th, 2019, 08:09 AM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 213 Thanks: 90 
Baseline answer: Let Aisling be the trendsetter. 1/7 chance that Brannon's birthday is the same day of the week. 1/7 chance that Caitlin's is the same. 1/7 chance that Dara's is the same. Chance of all four randomly being the same is 1/343 = 0.29 %. Now, twins, induced pregnancy/Caesarians, uneven likelihood of being born on each day of the week, etc. will affect this figure, but probably by a negligible amount. EXCEPT, saying, "every year," throws a monkey wrench into the works. There are two types of years  leap years and nonleap years. If all four dates are Jan 1  Feb 28, and they are the same day of the week one year, they will be the same day of the week every year. If all four dates are Mar 1  Dec 31, and they are the same day of the week one year, they will be the same day of the week every year. If some are in the former and some in the latter, they cannot be the same day of the week EVERY year. So for a revised estimate, we need to multiply the 1/343 times (the probability of all four falling in the first 59 days + the probability of all four falling in the last 306 days). (59/365.24)^4 + (306/365.24)^4 = 0.068 % + 49.269 % = 49.3 %. Estimated chance of all four members' birthdays falling on the same day of the week every year: 0.14 %. (As always, somebody check my maths.) 

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birthday, family, probability 
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