In a group of 23 people, the probability that two or more people will share their birthdays is greater than 50%. For a group of 57 people, this probability increases to 99%.
This may seem counter-intuitive at first sight. There are 365 possible days on which a birthday can occur. So it may seem odd that in a group of 57, there is 99% probability of a shared birthday.
Question: In a group of ‘n’ people, what is the probability that any of those ‘n’ persons shares a birthday with any of the others in the group?
This is very simple.
The answer is simply:
1 – (364/365) (363/365) … ((365 – n + 1 )/365 )
= 365 ! / [ (365^n) (365 - n)! ].
Approximating this function, and plugging in values of n, we get the probability of a group of those many people having a common birthday in their midst.
See http://en.wikipedia.org/wiki/Birthday_paradox for more on this.
2 comments
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September 24, 2009 at 5:54 pm
Sharadh
Ya you are right about the birthday paradox. I have read about this before, and at first sight it also seemed counter intuitive to me.
Your voter paradox was good, pardon me for not commenting there (wanted to club the comments together). I haven’t read about it before.
One small clarification: My blog doesn’t deal particularly with dharma (saw your categorization) even though I refer to the Bhagavat-Gita very often. I’m not telling you to change the categorization; just pointing out my opinion on my own blog.
Will read your thesis sometime later, whenever I have time. Till then, all the best.
September 24, 2009 at 6:21 pm
tkramesh
Hey, thanks for reading and commenting on this. Many such interesting topics are given at http://www.math.ucla.edu/~tao/puzzles.html.
You are right about your blog. I think I shall change the categorization to “Others”. Thanks for pointing it out.
You’ve been writing really good posts on your blog. Keep it up!