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 "orez" backwards in the box below (case sensitive):

Archive

Show me a random blog post
 2020 

Jul 2020

Happy τ+e-6 Approximation Day!

May 2020

A surprising fact about quadrilaterals
Interesting tautologies

Mar 2020

Log-scaled axes

Feb 2020

PhD thesis, chapter ∞
PhD thesis, chapter 5
PhD thesis, chapter 4
PhD thesis, chapter 3
Inverting a matrix
PhD thesis, chapter 2

Jan 2020

PhD thesis, chapter 1
Gaussian elimination
Matrix multiplication
Christmas (2019) is over
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2020