coloin wrote:see http://mathforum.org/dr.math/faq/faq.birthdayprob.html

There is a 50% chance that 2 out of 23 people will share the same birthday - therefore number of days in the year = 365 !

That's not quite correct, assuming that you meant to say "at least 2 out of 23 people", as per the standard bday problem (i.e. that you're simply inverting the standard bday problem, with the usual idealisations). Inverting the well-known solution for P(n,d), given the numbers you state -- i.e. solving for d in P(23,d)=0.5 -- does not lead to 365 as the number of days in the year:

- Code: Select all
`#people #days/year`

n d P(n,d)

------- ---------- ----------

23 365 0.50729...

23 366 0.50632...

23 367 0.50535...

23 368 0.50438...

23 369 0.50342...

23 370 0.50246...

23 371 0.50150...

23 372 0.50055...

23 373 0.49960...

where P(n,d) = 1 - d!/((d-n)!*d^n)

... "therefore there are about 373 days in the year."