How many people have to be in a class so that there is a 50% chance that at least 2 people have the same birthday?

Question

anonymous · Answer

is this a riddle?

saifoo.khan · Answer

it's a riddle.. satellite is stuck in the middle.. o_O

anonymous · Answer

xD

goformit100 · Answer

haha @saifoo.khan

amistre64 · Answer

more of a conundrum :)

a coworker is taking an online stats course and asked me this question

there is no "correct" answer that i know of, but is meant to exhibit intuition versus reality i think

anonymous · Answer

i will be quiet because i know the answer
will post a problem from dylan that took much of the morning

anonymous · Answer

Reality is a bit painful, I do say.

anonymous · Answer

oh so it is an honest question, not a riddle
answer is 23

lgbasallote · Answer

well i know if there are 366 people then 100% 2 people share same birthday :)

goformit100 · Answer

its easy

amistre64 · Answer

23 could be plausible, any logic to back it hto?

amistre64 · Answer

lgba, lol; yes 266 to be 100%

amistre64 · Answer

366 that is

anonymous · Answer

Logic is overrated.

amistre64 · Answer

but the "at least part"  hmmm

goformit100 · Answer

correct @amistre64

lgbasallote · Answer

then maybe 183 people then 50% chance? hehe

anonymous · Answer

I got this!

$$\huge1-e^{-x^2(730.5)}$$

anonymous · Answer

it is a calculation, for which you definitely need a calculator

anonymous · Answer

Yay for paying attention in class :D

amistre64 · Answer

id say intuitively, you need at least 2 people :)

anonymous · Answer

FYI: 365.25 days in a year

lgbasallote · Answer

but isnt that 1/365 x 1/365 chance? :O

amistre64 · Answer

thats what i thought too

anonymous · Answer

Leap year yo  :-P

anonymous · Answer

pass to the compliment, i.e. consider the probability that no two people have the same birthday
am using 365 with no stupid leap year to make calculation easier

amistre64 · Answer

ah yes, the compliment

anonymous · Answer

Aww nobody wants to dispute my expression eh? :-P

amistre64 · Answer

its a cute expression lol

anonymous · Answer

if there are say $n$ people then the probability no two people have the same birthday is 
$$\frac{365\times 364\times 363\times ...\times (365-n+1)}{365^n}$$

anonymous · Answer

@amistre64, I've never understood this. Why is your picture an integral?

anonymous · Answer

(I should also be asking why @satellite73 is using a bike.)

amistre64 · Answer

its not, thats my profile angle ;)

anonymous · Answer

now it is a matter of computing for various choices of $n$ and recalling that this is the compliment.

amistre64 · Answer

having a + sign just seemed to remedial

zepp · Answer

42.

anonymous · Answer

this is the bike that i took from amistre because he did not let me ride the bike they gave him for this 1000 medal (back in the day)

anonymous · Answer

You two have such a good relationship. I am jealous.

amistre64 · Answer

it tooks years of mistrust and antagonism to build this relationship as strong as it is lol

anonymous · Answer

he is the older brother i never had

zepp · Answer

o_o

zepp · Answer

Loki and Thor :D

amistre64 · Answer

cain and able is what i had pictured, but pagan dieties work too :)

anonymous · Answer

@agentx5  is that for real?

anonymous · Answer

Medalling @amistre64 for his contribution to @satellite73's brotherly needs.

anonymous · Answer

Is what for real?  The expression I wrote?

anonymous · Answer

i was thinking more of abbot and costello http://www.youtube.com/watch?v=KVn0aksCzNE&feature=related

anonymous · Answer

Every time I hear "for real" on this site, I immediately think of $\mathbb{R}$...

anonymous · Answer

If you make it into a standard y=f(x) function I believe it gives you the answer for any input, provided you use a ceiling or floor function to make it into whole #'s  :-)

anonymous · Answer

yeah the integral 
so probability you get no two birthdays the same with $x$ people is $e^{-750x^2}$?

anonymous · Answer

poisson?

anonymous · Answer

no that can't be it

anonymous · Answer

http://upload.wikimedia.org/wikipedia/commons/0/0d/050329-birthday2.png

anonymous · Answer

Of course somebody has already done this and uploaded it :-D  I was trying to give you all a graph in Wolf but it wasn't understanding what I was asking it to do I guess, kept graphing the wrong thing

anonymous · Answer

Hehe, now this is more interesting: http://en.wikipedia.org/wiki/Birthday_attack

radar · Answer

23 according to wikipedia

radar · Answer

http://en.wikipedia.org/wiki/Birthday_problem

radar · Answer

I knew that it was a surprisingly few, but didn't realize it could be that small of a number.