Coincidence and Probability

When I posted about Emila's 2010 Illustrated Calendar a few weeks ago, blogger Wan Lili of Suddenly, Heta! commented that she shares the same birthday as me. I was pleasantly surprised and noted that the chances of that to happen is quite low because this blog of mine doesn't really have that big a following.

Lili's comment reminded me of a programme I saw on The Discovery Channel some months back, about the probability of finding two persons within a group of people who share the same birthday. This problem is also known as the Birthday Paradox and there are quite a number of articles about it available on the internet. The different articles describe the problem in different ways but perhaps the simplest way that I can put it is as follows :

What is the minimum number of people needed within a group so that the odds of finding any two who have the same birthday becomes 50%?

Even for those of us who are mathematically inclined, the initial assumption we arrive at is that it must be a large number. There are 365 days in a year (ignoring leap years for simplicity)... and for 100% probability (i.e. a sure thing), we need 365+1=366 persons. Therefore, for an even chance of finding two people with the same birthday, the number is 50% of 366 or 183 persons.

This answer is wrong. Probability theory shows that we only need to gather 23 persons for the odds to become even (i.e. 50:50 chance). Now how can this be? I don't want to bore you with the mathematical analysis of this problem but you can read the links I've included below for detailed explanations.

This phenomenon is not actually a paradox in the logical sense of the word but it seems so to most people because the mathematical truth contradicts natural intuition. The human brain thinks of progression and extrapolation generally in linear terms and gets confused when some things expand on an exponential basis.

In the second reference article below, Robert Matthews and Fiona Stones carried out a study to test this theory by looking at football matches. In a football match, you can find 23 people i.e. 11 players from each team and the referee. If there are 10 such matches, then probability theory says that we should be able to find birthday pairs in 5 of them (50:50 chance). Matthews and Stones did their analysis on 10 Premier League fixtures played in 19 April 1997. It involved them checking the birthdays of 220 players and 10 referees. Sure enough, they found that there are coincident birthdays in 6 of the matches. In fact, they found two pairs in 2 of the fixtures.

To extend slightly on this subject, the theory also says that we need only 57 people for the probability of any two people with coincident birthdays to become 99%. In other words, if there is a gathering of around 60 persons, I'm willing to bet that I can find at least one pair that share the same birthday.

Graph from Wikipedia, showing the approximate probability of at least two people sharing the same birthday amongst a certain number of people

I did a bit of my own analysis on this matter using the birthdays of my Facebook friends. I compared their birthdays against the sequence of when we became friends. The result is pretty close to the theory. The 24th person who became my FB friend shares the same birthday with the 9th person. I did not have to wait long for the second pair. The 28th FB friend has the same birthday as the 22nd friend.

I was about to do the same analysis on the extended family on my wife's side (parents, siblings, in-laws, nephews, nieces etc.) but then realised that the same-birthday occurrence is found even earlier. My father-in-law (the no. 1 guy) has the same birthday as his youngest son (the 15th family member).

To use the conclusion of the Matthews & Stones research, coincidences really are “out there”, as probability theory predicts, if we take the trouble to look.

References :

1. Birthday Problem - Wikipedia
2. Coincidences : the truth is out there

Last weekend

This post is a bit outdated. I've been meaning to upload the pics much earlier but I was under the weather for the past few days. Just posting something so that this blog is not neglected for too long.

We were in Singapore last Sunday to attend the wedding reception of the niece of an old friend and classmate. I have not met this friend for more than twenty years and it was nice to be meeting him again and catching up on old stories.



In Malay wedding ceremonies, the procession of the bride and groom is normally accompanied by a kompang group. In this instance however, the family opted for a kuda kepang troupe. First time that I've seen this and it does make an interesting difference.



Later that evening, I decided to take a drive down Orchard Road just to have a look at the Christmas lights. It has been quite some time since I was last in the area and the changes are quite surprising. The beautiful lights gave photographers ample chance to practice their night photography skills. Makes me wish to get my hands on a DSLR soon...

To all muslim friends and readers, selamat menyambut tahun hijrah yang baru.

Conversations

She was sitting across him in the cosy restaurant of a 5-star hotel. Her hands were twisting the teacup on its saucer, a clear sign of edginess.

`You’ve not finished your dessert,’ he says, looking at the half-eaten apple pie on the small plate on the table.

`I am not actually hungry,’ she responds. He just nods, sips his coffee and looks at her in silence. It is obvious that she wants to say something but probably finding it hard to know where to begin. The restaurant is practically quite now, with most of the lunch crowd already gone.

She takes a deep breath and then asks, `Why are you leaving?’

`It is time to do so,’ he answers with a subtle shrug of the shoulders.

`There must be more reasons than that?’

`Yes, there are I guess… but it won’t make a difference for you to know.’

`Uh-huh… who am I to be asking you these things, right?’, she rhetorically asks in a resigned tone.

He does not give an answer... because he knows there isn’t a correct one.

Four Fridays on a trot

If you make your living in the state of Selangor, you would be enjoying public holidays on the next 4 consecutive Fridays :

1. 11 December 2009 (Friday) - Sultan of Selangor's Birthday
2. 18 December 2009 (Friday) - Awal Muharram
3. 25 December 2009 (Friday) - Christmas Day
4. 01 January 2010 (Friday) - New Year's Day

That's four long weekends on a trot. You could use the time to go for a mini-break, to catch up on some reading, send your young son for his berkhatan ritual, attend wedding invitations or perhaps organize one of your own...

I bet the TGIF restaurant chain is really looking forward to this.

A good look at books

One of the things I loved about living in KL a few years back is the ability to browse for hours at the Kinokuniya bookstore in KLCC. While I don't actually buy that many new books, spending time flipping through pages of published text and photos is something that I quite like to do. For the buying part of it, I would normally go to the discount bookstore at Ampang Point. Additionally, warehouse book sales are events that I try not to miss.


In Johor Bahru, the only bookstore with a sizeable spread of books is Harris at Jusco Tebrau City. Harris is part of the Popular Book Store group.

This week, Popular Book Store organised a book fair at Danga City Mall and today is the last day. We made our way to the fair this afternoon and picked up a few books that were sold at significant discounts. My wife and I selected 3 books each while my son picked up 2 . I actually wanted to get a few more but I doubt I have the time to read all of them soon. There are still some books that I bought at a Times warehouse sale in PJ three years ago that remain in packing boxes.

All my choices are fiction. Two recent and one old. I had also wanted to get a Charles Dickens classic to re-read but while other titles from Dickens were available, The Tale Of Two Cities was not.

Of the recent books, one is called The Reluctant Fundamentalist by Pakistani author Mohsin Hamid. I got to know of this book through blogger Dr Wati who posted about it last month. At only RM19.90 less 20% discount, it is a steal.

The books that I've bought today would probably cover my reading appetite for the next two months. After that, I'll be on the look-out for other book sales or maybe even find an excuse to make a trip to Ampang Point.