The Birthday Paradox

Recently two of my friends (and neighbours) in the village noticed that they shared a birthday. They expressed surprise at this revelation because it seems improbable. Actually it is likely that a relatively small group of people will have two members with the same birthday. For instance, with groups of 25 people, two will have birthdays on the same day of the year in 56% of cases; with groups of 60 the likelihood increases to more than 99%. These apparently unlikely facts can be demonstrated by some simple maths.

The simplest way to start this is to investigate the likelihood that people do not have the same birthday. The probability t hat two people do not have the same birthday is 364 / 365 , as there is only one chance in 365 that one person's birthday will coincide with another's). The probability that a third person's birthday will differ from the other two is 363 / 365; a fourth person's 362 / 365; a fifth person's 361 / 365; ans so on to the fraction for the 25th person which is 341 / 365. This gives us 24 fractions that have to be multiplied together to reach the probability that all 25 birthdays are different. This gives a percentage of 43.13%. Given that there are only two alternatives, either no birthdays match or two (or more) do match. Therefore the probability that there will be a match is 100 - 43.13 = 56.87%

I calculated these percentages in a spreadsheet. The formulas that I used are shown in the picture below. (Naturally, just enter them in row 3 and fill down.)



For a larger and clearer version click on this link.
I also charted the spreadsheet. The probabilities can be read off the chart below:



For a larger and clearer version click on this link.

So what to make of my friends' birthday coincidence. There are eleven people living in our street. If we just consider this group the birthday coincidence is relatively unlikely at 14% though not at all impossible. If you consider the wider village with almost 150 people it is virtually a certainty that two people will have the same birthday. Although I haven't checked, I expect that there is likely to be at least one other birthday coincidence.

Michelle Obama answers the question on everyone's mind

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Hot

I had planned this post as a recording of the hottest day in Melbourne's history. As the day unfolded it became something else .....

The photo below was taken yesterday on our back veranda.



Nice veranda, but nothing particularly remarkable there, you might say. The round object on the wall is a thermometer.

Take a close up view.




Yes that does read 50 degrees Celsius!

It might not have been quite as hot as that. A Bureau of Meteorology weather station, a few kilometers away from us recorded a daily maximum of 47.5 degrees Celsius. In Fahrenheit that is 117.5 degrees.

The official Melbourne maximum temperature was 46.4 degrees, which is 115.5 degrees Fahrenheit.

This was the highest maximum temperature in Melbourne ever recorded.

Before yesterday the highest temperature was 45.6, set on January 13, 1939. It came to be called Black Friday . That was before I was born, but I remember my parents often mentioning it when I was young.

Black Friday had the worst bush fires in Australian history, when 71 people were killed.

After the 1939 fires, many changes were implemented to stop a repeat of the devastation.

But ...
the devastation caused by the bushfires yesterday is far worse that that of Black Friday.
Currently the death toll from yesterday's fires is over 100 people and rising with many houses destroyed and in a few cases whole towns.

It is horrific.

Tamino at one of my favourite blogs, Open Mind, has a post that includes information on warming in Melbourne over the last century and some comments on its relationship to Global Warming and Climate Change.

Barry Brook of Brave New Climate blog quotes an Australian Meteorologist in this post:

Given that this was the hottest day on record on top of the driest start to a year on record on top of the longest driest drought on record on top of the hottest drought on record the implications are clear...

It is clear to me that climate change is now becoming such a strong contributor to these hitherto unimaginable events that the language starts to change from one of “climate change increased the chances of an event” to “without climate change this event could not have occured

Istanbul photo contest

During our trip to Europe last June we visited many iconic European cities. Our favourite surprised us though; it was Istanbul.

It is a fantastic freewheeling city a mesmerising mix of East and West.

It is also wonderfully photogenic.

I was happy with some of the photos that I took there, but none came close to the stunner below:




It is the winner in the Istanbul Photo Contest of 2008.

Here are a few of my Istanbul photos. Sadly no comparison.



Inside the Blue Mosque.



Saint Sophia surrounded by the bustling city.



Margaret shopping in the Grand Bazaar.

Poor Boy

Yesterday we saw our second MTC play for the season: Poor Boy; a gentle fable about reincarnation and redemption.

Here is a summary of the plot from a review in the Age:

Matt Cameron and Finn have created a ghost story of some eeriness and intensity. Jeremy Glass is a boy who, on the eve of his seventh birthday, insists he is the reincarnation of a dead man, Danny.

Jeremy's parents, Viv (Linda Cropper) and Sol (Greg Stone), are understandably disturbed. But when the boy seeks out Danny's mother (Sarah Peirse) and his family, and recalls details of Danny's former life that he couldn't possibly know, Jeremy's family begin to think they have lost their child forever. As the families converge, the secrets of the living and the dead are revealed.

There were three elements about this production that drew attention:

The Venue
The fist play at the MTC's new Sumner Theatre.


The Music
The play features songs by Tim Finn, but it is more a "play with songs" than a musical.
Here are videos of two of the songs. (Obviously not from the play).

Poor Boy, a Split Enz version.



In a Minor Key, with Tim at the piano.




The Cast
Especially Guy Pearce, who plays the ghost of Danny. The photo below is the publicity shot.


Here is a slide show showing some of the scenes from the show:



There have been some critical reviews; for instance Australian Stage Online claimed:

... there is a pervasive sense that the songs, written over nearly thirty years and not created with theatre in mind, have been imposed on the story, or vice versa; there is simply no necessary link between the two elements at many points, the plot and characterisations are effectively suspended by the music, or a pleasant concert interrupted by an extraneous story line. At two and half hours, attention begins to flag. Moreover the actors have variable success with the music, some singing more in character and with more ability than others, but none aided by an often too-loud band.

Even if there is some truth to that opinion, both Margaret and I enjoyed the play, finding the plot, acting, staging and singing very satisfying.

One further item of interest: we are always looking for points in common with residents in our village, and when waiting for this show to start we noticed one of our fellow residents, Del. We discovered that she is also a long standing subscriber to the MTC plays.