My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 12th, 2019, 12:36 AM   #1
Newbie
 
Joined: Sep 2019
From: Washington State, USA

Posts: 1
Thanks: 0

Question 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.
hendersonrobyn is offline  
 
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 non-leap 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.)
DarnItJimImAnEngineer is offline  
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
birthday, family, probability



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Family with 5 children probability taylor_1989_2012 Probability and Statistics 8 October 30th, 2016 03:26 PM
Probability of group having a birthday on every day of year daigo Probability and Statistics 2 February 2nd, 2012 12:16 PM
Birthday Probability BobSmithIV Advanced Statistics 1 April 14th, 2011 08:33 PM
Birthday Probability meph1st0pheles Advanced Statistics 2 January 28th, 2010 06:09 PM





Copyright © 2019 My Math Forum. All rights reserved.