Last week, on http://www.guardian.co.uk, there was a nice post on coincidences, concluding with “a decent knowledge of mathematics shows you that most coincidences are just that: coincidence“, asking for a better knowledge of basic probabilities….
The only problem is that the first line is not correct… “Today is my birthday, which means that there is a 50% probability that one of the first 23 people who read this blog entry will share their birthday with me”.
There is a well known “paradox” in probabilities related to this: the correct sentence should be “there is a 50% probability that if we consider the first 23 people who read this blog entry at least two of them will share their birthday“… but not necessarily with you… Indeed the probability that 2 people out of 23 share their birthday is
> 1-prod(365:(365-22))/(365^23)  0.5072972
But if you want to find someone who share his/her birthday with you, you need to wait for the first 253 if you are looking for 50% chances,
> 1-(364/365)^253  0.5004772
But dealing with probability is not that simply. At least, we get the message… And I will be the last one to blame you: yesterday, a colleague got me asking me “simple” questions about probabilities to find a pair a socks in a several drawers… And I could not get it right…