### Math appreciators.

Gauthak

Senior Member

Here goes a nice challenge for you.

In a group consisting of n persons, what is the probability of there being any birthday coincidence?

Consider the year in question a 365 days one.

Loammi

Member

The probability of 2 people having the same birthday is 1/365. The probability of a group of 3 people having AT LEAST 2 people with coinciding birthdays would be 1/365 times 3 (it could persons A and B, A and C, or B and C) plus the probability that all three of them have the same birthday (1/365)^2

That should get you started on your homework...

Senior Member

Quote:
Originally Posted by Gauthak
Here goes a nice challenge for you.

In a group consisting of n persons, what is the probability of there being any birthday coincidence?

Consider the year in question a 365 days one.

You would need to first define what constitutes a birthday coincidence. Same day of the month, same day of the year, exact same date, same hour, etc.

Keshaldra

Senior Member

Quote:
You would need to first define what constitutes a birthday coincidence. Same day of the month, same day of the year, exact same date, same hour, etc.
The traditional problem dictates same day of the year.

Dobagoh

Member

Quote:
Originally Posted by Loammi
The probability of 2 people having the same birthday is 1/365
This is false.

People are more likely to be born during the spring and fall months (humans have "breeding seasons" during the summer and winter seasons, so that babies are more likely to be born when food is plentiful. The probability of 2 people having the same birthday, is thus dependent on when they were born, and is not equal to 1/365.

Gauthak

Senior Member

Quote:
Originally Posted by Dobagoh
This is false.

People are more likely to be born during the spring and fall months (humans have "breeding seasons" during the summer and winter seasons, so that babies are more likely to be born when food is plentiful. The probability of 2 people having the same birthday, is thus dependent on when they were born, and is not equal to 1/365.
Agh. And i tought it wouldnt be necessary to say to disregard any not math related stuff.

And its not my homework.

Worstcase

Senior Member

Technically the only way for it to be 100% guaranteed is through pigeon-hole. As in at most there could be 365 kids with different birthdays, and the 366th 'must' have a pair (assuming no leap year). Now the probability of say, 23 kids having the same birthday is interestingly enough 50%. Contrary to what I said earlier, and there are a couple factors for this, one was already stated.

JacobianMatrix

Senior Member

Quote:
Originally Posted by Dobagoh
This is false.

People are more likely to be born during the spring and fall months (humans have "breeding seasons" during the summer and winter seasons, so that babies are more likely to be born when food is plentiful. The probability of 2 people having the same birthday, is thus dependent on when they were born, and is not equal to 1/365.
The problem assumes a uniform distribution.

Assuming the uniform distribution, the probability of a mutual birthday (ignoring February 29th) P(n) is :

P(n) = 1 - (n!(365-choose-n))/(365^n)

where

365-choose-n = (365!)/((n!)((365-n)!))

By the pigeonhole principle, this probability is 1 if there are 366 or more people in the room.

Dobagoh

Member

Quote:
Originally Posted by JacobianMatrix
The problem assumes a uniform distribution.
so does your face after i've beat it for a year