A Probability Question (Humans)

by xeno6696 , Sonoran Desert, Sunday, July 31, 2011, 14:57 (4660 days ago) @ David Turell

Not sure if I ever posted this one, but it just came to mind as I was taking security training. If you remember the answer, wait and spoil it later...
> > 
> > If there is 30 people in the same room, what is the probability that any two individuals have the same birthday?
> > 
> > This question underlines the slippery nature of probability, and the importance of asking the right question.
> > 
> > The answer to this is available, however I hope you try this on your own before going to google/Bing/Baidu...
> 
> I would guess 1 in 24-Well, you're the only one who's interested, so I'll go ahead and explain the results. -The answer is a Probability P(.70) or 70%. If you have 23 people, it's P(.5) and at 57 you reach P(.99) or 99%.-Why so high? There's 365 days of the year, right? so assuming all birthdays are equal, the probability would intuitively be 1/365 * 1/365. (A basic rule in probability is that the probability of two events ocurring is the probability of both events, multiplied.) But that only supplies part of the model. -The key here is that our minds don't phrase the question properly: If you randomly select two people from the room, you only have two choices--either they share the birthday or they don't. P(.50) So the question becomes, "How many people, when the probability of them sharing a birthday is .50, do you need to guarantee an arbitrary probability?"-All the steps to compute the probability are here and are actually quite easy. -The link also shows some diagrams that plot the probabilities for various numbers of people. This doesn't have an immediate effect on our discussions, but my first answer to that problem some years ago was just as incorrect as your own... and probability is quite possibly the trickiest area of mathematics, hence why I'm always so damn cautious when people throw numbers around... I don't trust the numbers without having direct access to their calculations and work.

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"