View Full Version : Odds of birthday on same day

MrConfused

02-17-2010, 05:08 PM

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 ?

:confused:

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 ???? :confused:

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

Thanks.

Outlier

02-17-2010, 06:37 PM

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

MrConfused

02-17-2010, 11:11 PM

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?

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:yup:

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/blog5.php/when-are-most-babies-conceived

:eek:

MrConfused

02-18-2010, 12:53 AM

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:yup:

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/blog5.php/when-are-most-babies-conceived

:eek:

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

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

02-18-2010, 01:07 PM

However, I Bill and Andy are twins, then

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

It is possible for twins to be born on different days ;)

talkstatsdkf

02-18-2010, 02:23 PM

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%21%2F335%21%29+%2F+%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=%28364%2F365%29%5E%28C%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/260341-ap-statistics-introduction-and-descriptive-statistics

(my other posts on talkstats)

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

Outlier

02-18-2010, 03:09 PM

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

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

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