/sci/ - Science & Math

>>7045190

How is it a paradox?

Anyway, you need to think about it in terms of how many different PAIRS of people there are. If we think of it in terms of (x,y), for x we have 23 options, then we need to go on to choose y. We have one less person to choose from, so we have 22 options.

Thus, in total we have 23 * 22 options for pairs of people, BUT you have to remember that when we count this way, we have counted each pair twice. Say that we counted Dave for our first spot, and John for the second. We also have a pair where we counted John for our first spot, and Dave for our second. So, we need to divide by 2 to give us our actual number of pairs. So, our total number is (23 * 22) / 2, or 203. So, in total we have 203 opportunities for overlap in birth dates. 205/365 is greater than 1/2, and that's how we 23 people in the same room have greater than 1/2 chance of having the same birthday.

Start with 1 person, with birthday B1.

Add another. Three hundred and sixty four times out of three hundred and sixty five, we have no match. This guy has birthday B2.

Now add a third. His birthday might match B1 and might match B2, but 363/365 times it won't. Call his bday B3 and move on.

Chance of no match at this point: 364/365 * 363/365.
Add a fourth person and the chance of no match is multiplied by 362/365. Add a fifth and multiply by 361/365.

Follow down and the net chance of no match for 22 people is 52.4%, but for 23 it's 49.3%. A match is now more likely than not.

may 10

>>7045222
november 27

>>7045224
January 14

>>7045190
Ok, here's another route to calculate it.

For the second person to not have the same birthday as the first, theres 364 acceptable bdaypicks. For the third, there's a 363 left to choose and so on.

(365!)/(365-x)!/365^x = 0.5 has one positive solution x = 22.767...

>>7045227
April 19
This may take a while
Anyone want to make a /b/read about "if birthday match, play vidya/hook up/whatever" to use for data

June 15

October 10

July 25

February 19

June 25

May 16

July 13

November 13

Sexspermber 98th

december 24

>>7045257
ding

Gay 69

>>7045283
Only took 14 people.

>>7045198
That's not how it works. If A and B don't match and B and C don't match, what's the chance that A and C match? 0

>>7045299
inequality isn't transitive faggot
I like your dubs though

Dank memes

November 11th

>>7045299

haha wot?

if person A= 1 dec and B= 2 dec and C=1 dec
A=/=B, and B=/=C but A==C
How hard is that?

>>7045198
First of all 23*22/2 is not 203. And where did you get 205 from?

It may be true that we have 22*23/2 possible pairs. But from there, how do you build the relation to birthdays?

It is easy to see that your argument is absurd. Find N such that N*(N-1)/2 is larger than 365.

What would that mean? Larger than 100% chance of overlapping b-days? How would that be interpreted?

>>7045386
>It may be true that we have 22*23/2 possible pairs. But from there, how do you build the relation to birthdays?
Given two people, what's the chance of them having the same birthday? 1/365.
Given 23 people, how many distinct pairs can you make? 23*22/2 = 253.
Therefore, given 23 people, the chance of two of them having the same birthday is 253 * 1/365.

>>7045292
That's surprising seeing as we're on 4chan where you would expect people to be smartasses and either have it happen with the first two or list all 366 dates without a match.

Is this maths really so difficult to understand.

1 guy has a bday at some date.

you bring in a new guy. the chance of him having a bday at the same date is 1/365.

unless they share a birthday, add a new guy. his chance of having a birthday at the same time as any of the other two, is 2/365 now.

keep going. add the possibilities together, meaning:
1/365 + 2/365 + 3/365 ... to 23 people means

(1+2+3...+23) / 365.

turns out if you sum 1 to 23 you get about half of 365, or if you want it from the other point of view, by the time you have added 1 to 23 you have reached 50% of 365.

It shouldn't be that hard to accept.

>>7045410
Ok so take 50 people. 50*49/2, that's a lot more than 365 which would mean a probability of more than 100% which is impossible, because then it isn't a probability.

>>7045450
Lol. Just stop. You are embarrasing.

>>7045221

This is the best breakdown of it that I've seen.

>>7045222
you mother fucker :D
no one else noticed your joke, but I did.

>>7045552
Please enlighten me! Matein' or what?

>>7045562
see
>>7043585

This sunday

>>7045227
January 14 as well
>>7045604 happy birthday for Sunday anon