mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

 2013-07-24 
A news story on the BBC Website caught my eye this morning. It reported the following "uncanny coincidence" between a Northern Irish baby and a Royal baby:
But both new mothers share the name Catherine, the same birthday - 9 January - and now their sons also share the same birth date.
I decided to work out just how uncanny this is.
The Office for National Statistics states that 729,674 babies are born every year in the UK. This works out at 1,999 babies born each day, assuming that births are uniformly distributed, so there will be approximately 1,998 babies who share Price Nameless's birthday.
So, what is the chance of the mother of one of these babies having the same birthday as Princess Kate? To work this out I used a method similar to that which is used in the birthday "paradox", which tells us that in a group of 23 people there is a more than 50% chance of two people sharing a birthday, but that's another story.
First, we look at one of our 1,998 mothers. The chance that she shares Princess Kate's birthday is 1/365 (ignoring leap days). The chance that she does not share Princess Kate's Birthday is 364/365.
Next we work out the probability that none of our 1,998 mothers shares Princess Kate's birthday. As our mothers' birthdays are independent we can multiply the probabilities together to do this (this is why we are looking at the probability of not sharing a birthday instead of sharing a birthday). Our probability therefore is \(\left(\frac{364}{365}\right)^{1998} = 0.00416314317\).
Back to the original question, we wanted to know the probability that one of our mothers shares Princess Kate's birthday. To calculate this we do take 0.00416314317 away from 1. This gives 0.99583685682 or 99.6%.
There is a 99.6% chance that there is a resident of the UK who shares the same birthday as Princess Kate and had a child on the same day.
Uncanny.
But let's be fair. The mother in our story is also called Kate. So what are the chances of that? In fact, the same method can be followed, working with the probability of having neither the same birthday or name as Princess Kate.
I think it is safe to assume that this would still be considered news-worthy if our non-princess was called Katie, Cate, Cathryn, Katie-Rose or any other name which is commonly shortened to Kate, so I included a number of variations and used this fantastic tool to find the probability of a mother being called Kate. The data only goes back to 1996, but as the name is dropping in popularity, we can assume that before 1996 at least 1.5% of babies were called Kate. Disregarding males, we can estimate that 3% of mothers are called Kate.
If anyone would like the details of the rest of the calculation, please comment on this post and I will include it here. For anyone who trusts me and isn't curious, I eventually found that the probability of none of our 1,998 mothers share the same name and birthday as Princess Kate is 0.84855028964. So the probability of another Kate having a child on the same day and sharing Princess Kate's birthday is 0.15144971035 or 15.1%. Just over one in seven.
So this is as uncanny as anything else which has a probability of one in seven, such as the Royal baby being born on a Monday (uncanny!).

Similar posts

World Cup stickers 2018, pt. 3
World Cup stickers 2018, pt. 2
A bad Puzzle for Today
A 20,000-to-1 baby?

Comments

Comments in green were written by me. Comments in blue were not written by me.
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li>
To prove you are not a spam bot, please type "r" then "a" then "t" then "i" then "o" in the box below (case sensitive):

Archive

Show me a random blog post
 2021 

Jan 2021

Christmas (2020) is over
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

noughts and crosses braiding electromagnetic field convergence bubble bobble probability talking maths in public binary tennis final fantasy gaussian elimination people maths royal institution pythagoras sorting matrix multiplication geogebra arithmetic harriss spiral advent calendar matrix of cofactors interpolation bodmas graphs wave scattering pac-man asteroids golden spiral dataset ternary propositional calculus go books sport folding paper phd stickers games video games boundary element methods weather station big internet math-off preconditioning countdown statistics cambridge light coins exponential growth weak imposition sound draughts mathslogicbot palindromes pi approximation day rhombicuboctahedron frobel accuracy php national lottery martin gardner map projections inverse matrices radio 4 london underground python menace chebyshev matrices simultaneous equations hexapawn approximation chalkdust magazine reuleaux polygons nine men's morris signorini conditions logs reddit matt parker european cup raspberry pi manchester latex ucl dragon curves tmip captain scarlet polynomials realhats gerry anderson royal baby a gamut of games world cup puzzles christmas flexagons machine learning numerical analysis estimation mathsteroids graph theory speed hats fractals manchester science festival javascript triangles error bars finite element method geometry london game of life trigonometry data misleading statistics matrix of minors pi bempp oeis cross stitch pizza cutting curvature squares programming quadrilaterals christmas card rugby dates logic computational complexity mathsjam plastic ratio folding tube maps football determinants game show probability data visualisation platonic solids chess inline code twitter wool hannah fry news golden ratio the aperiodical sobolev spaces craft

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2021