The limitations of common sense

How many people do you need at a party before the probability of there being a shared birthday reaches 50%?Common sense answers only

Nice one 50% is exceeded at 23, so that is the correct "answer" though as you say, real world clustering of birthdays, and the odd pair of twins are going to lower this very slightly.The important point is this is about the size of one of my maths sets. It's a good bet to play with them that two of the students share a birthday...I would love to see the reasoning that led to 5 though

I love your thinking Omni... I always told my students that poker taught a great stats lesson For those wanting to know how to calculate, these problems are nearly always much more tractable by reversing them. One shared birthday solves this, but so does two shared birthdays, or three peopel sharing one birthday. There are many many permutations and it is very difficult trying to account for them all. Far easier is to look at there being no shared birthdays:First person can have any birthday: 365 possibilities
Second person can have any birthday but the first: 364 possibilities
Third person has 363 possible days
Fourth has 362 days to choose from
etc, etcSo probability that 5 people do not share a birthday is:

365   364   363   362   361
--- x --- x --- x --- x --- = .973
365   365   365   365   365

and so prob that there is at least one shared birthday is 1 - 0.973 = 0.027 Fairly lowSo just keep adding more people and more terms to the above product and wait for the answer to drop below 50%, which happens with 23 terms, and so 23 people is the answer...This message has been edited by cavediver, 04-10-2006 04:52 AM

"perfectly stationary" only can really mean with respect to our local comoving frame in the universe, so you are going to find yourself about 15 million miles from the earth... possibly well on your way to Mars

I think there's an entire topic here, in what leads to "common sense" conclusions: false memory, false reasoning, and may own favourite and short-coming: false assumptions...

Ok, this is what we can call the error of assumption of linearity. There must be many examples of this in everyday life...The actual answer is between 14 and 16, depending on how many of the birthdays actually fall within two days of each other (as two birthdays a day apart only restricts 5 days from the calendar, not 6)