Odds of birthday on same day

[MrConfused]

I'm confused about the following...

Two people have their birthday on a specific day of the year. Are the odds 1:365 or 1:730 ?



I'm probably wrong but I think it is 1:730 for two people to have their birthday on a specific day of the year and then 1:365 for two people to have their birthday on the same day, any day of the year, not on a specific day.

Then if that is correct that both being on the same day (any day) is 1:365, then that occurance of both being on a specific day is another 1:365. Or for both to be on the same week is 1:52, or for both to be during a specific week 1:417 ????

I'm also having low blood sugar from dieting, so excuse my stupidity.

Thanks.

[Outlier]

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

[MrConfused]

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

I found the "Same birthday as you" on that page. But I didn't find the same type of problem.

So I will rephrase my question to make it clearer:

The odds of Andy having a birthday on the same day as Bill is 1:365. But the day has not been determined in this problem.

So my question is, on a determined day...

The odds of Andy having a birthday on Feb 18th is 1:365.

The odds of Bill having a birthday on Feb 18th is 1:365.

The odds of BOTH Andy and Bill having a birthday on Feb 18th?

1:730?

[fed1]

If Bill and Andy are unrelated then

Pr[ Bill on day i and Andy on day i ]

== Pr[ Bill on day i ]Pr[ Bill on day i ]

==(1/365)^2

However, I Bill and Andy are twins, then

Pr[ Bill on day i and Andy on day i ] == 1. For obvious reasons

It is also worth bearing in mind that births are not uniformly distributed across days of the year. This article gives more insight on this strange phenomenon

http://www.toucanlearn.com/blogs/blo...bies-conceived

[MrConfused]

If Bill and Andy are unrelated then

Pr[ Bill on day i and Andy on day i ]

== Pr[ Bill on day i ]Pr[ Bill on day i ]

==(1/365)^2

However, I Bill and Andy are twins, then

Pr[ Bill on day i and Andy on day i ] == 1. For obvious reasons

It is also worth bearing in mind that births are not uniformly distributed across days of the year. This article gives more insight on this strange phenomenon

http://www.toucanlearn.com/blogs/blo...bies-conceived

Thanks that is interesting. Based on that info, Oct-Dec seems to be the happening time in the bedroom

But does (1 / 365)^2 take into account that Bill's birthday (day i) is known?

If I know my birthday is Feb 18th, then the odds of me finding out that the random person I'm talking to on the phone shares my birthday is 1/365.

But if I select two people at random, the chances that they both have the same birthday on a specific date that I have in mind, is (1/365)^2?


To sum this up:

1) the probability of two people sharing the same birthday on any given day is 1/365. We just don't know what their birthdate is.

2) the probability of two people sharing the same birthday on a specific date such as 2/18 is (1/365)^2, if you consider that it took 1/365 for person A to be born on that date, and it also took 1/365 for person B to be born on that date.

THIS is where I'm confused.

[Martingale]

However, I Bill and Andy are twins, then

Pr[ Bill on day i and Andy on day i ] == 1. For obvious reasons

It is possible for twins to be born on different days

[talkstatsdkf]

People often call the Birthday Paradox the observation that it doesn't take a large number of people for the probability that two people will have the same birthday to be fairly large.

If we have a class of 30 people the probability that all birthdays will be different is (this analysis ignores the issue of Leap Day (February 29)):

1st___________2nd________3rd_______________30th
(365/365) * (364/365) * ( 363 / 365 ) * .... ( 336 / 365 )

which is about:

0.29

http://www.wolframalpha.com/input/?i...28365%5E30%29+

So here's a little puzzle:

Could you analyze it as C(30,2) trials (consider each possible pair of students) and say that the probability of them not having the same birthday is:

364/365

so the answer would be:

(364/365)^( C(30,2) )

however, that is about one hundredth more than 0.29, it's about:

0.30

http://www.wolframalpha.com/input/?i...2830%2C2%29%29

So the puzzle is: why does that analysis overestimate the probability of all different birthdays?

David

p.s. Please consider attending my lecture on Sunday at 2:00 p.m. on wiziq:

http://www.talkstats.com/showthread.php?t=10984

http://www.wiziq.com/online-class/26...ive-statistics

(my other posts on talkstats)

http://www.talkstats.com/search.php?searchid=335034

[Outlier]

Oct-Dec seems to be the happening time in the bedroom

The longest pregnancy recognized in a court of law might be one year, but this was before DNA testing.