Mike Floorstand's discussion below prompted me to write this. There is, as he said, a probability of greater than 50% of two people sharing a birthday in a room of 23 people or more.
Well, there are lots more than 23 people on this site, so when are your birthdays?? Mine is January 11th.
Last day of the fiscal year, and the day that all the coupons expire.
I teach statistics and probability, and last semester I offered to bet that there were at least two students in my class of 34 who shared a birthday. (There was around an 80% chance I'd be right.) My students, who apparently spend many weekends losing money at the local casino, all offered to take me up on the bet. They were so certain that they were right that they were willing to bet against their probability teacher. Not even the pair of twins in my class thought it unwise to bet against me. *sigh*
Whats the chance of two people with consecutive membership numbers having birthdays on consecutive days?
(From what I've seen on this site over the years I know there's someone out there who will rise to this challenge for us, so the rest of us can get on with our lives)
"Whats the chance of two people with consecutive membership numbers having birthdays on consecutive days? "
Assuming you mean 'at least two....' the answer changes as membership grows (gets more likely). I think you have to do it by working out the chance that >=2 do NOT have the same birthday (then take that away from unity)
ie chance that member #2 is NOT on Feb 26 AND
chance that member #3 is not on day after #2 AND etc
is (364/365)^52846 ignoring leap years
ie VERY small (about 1.1*10^(-63) )
In fact you only need a membership of about 250 for you to have a 50:50 chance of consecutive members having consecutive birthdays
In answer to Jerry O'Donnell's question: somewhat. The probability that 36 randomly chosen birthdays omit at least 4 months is approximately 1.6%. The chances of them omitting 4 specific months are about 32 out of a million.
In answer to showaddydadito: ignoring Feb 29 (which wouldn't change the answer by much), it's 1-(363/365)^(number of members). This number is something like .9999... with about 127 nines before it has a different digit.
..but Gary, the 363/365 in your formula allows for the member with higher membership no. to have the "LOWER" birthday. Maybe that's ok, maybe not . (who cares?)
.and as for 32 out of 1000000, isn't it just (8/12)^36 for specified months? ie .45 out of 1m?
Anyway, I can see a stern email coming our way with instructions to do penance by now posting 10^6 ITM related comments/discussions
Domnull - whoever sends that email had better copy it to everyone, including the guy who put the eighth post on this discussion - someone called Jeremy.
well 127 years ago James Joyce was born, author of one of the most controversial books ever written 'Ulysses' (1922) _ bit of an irish connection
to me, by way of further deviation the following musicians are :
84, Elaine Stritch, actor and singer
65, Sir Andrew Davis, conductor
51, David Newton, jazz pianist and composer
41, Simon Wickham-Smith, musician and astrologer
38, Michelle Gayle, singer and actor
to me, i go with Bernard Baruch's :
'To me, old age is always 15 years older than i am.'
Sorry for the delay, Domnull; had to get dressed, drive 20 miles, and teach two classes in the last 3 hours. Yes, the 363/365 is because the question didn't require the higher member number to have a later birthday, just to be consecutive.
(8/12)^36 is for omitting a specific 4 months. (But I screwed up and used 8/12=.75 instead of .666...!) Sorry.
Also, omitting any 4 months is quite a bit more likely than omitting 4 specific months. Still, I screwed that one up. I just did it as C(12,4)(8/12)^36 (with the same arithmetic error), when it should really be a complicated inclusion/exclusion formula.
Reverend - amazingly enough, aside from the twins, there was another pair of students with the same birthday (different years), and one student had the same birthday as me! Now THAT I wouldn't have bet on.
April 6th.
Same as Ian Paisley ( well, that proves astrology can't be right, just for a start ), Paul Daniels ( an annoying illusionist ), Andre Previn, and Rory Bremner.
I really was born yesterday (Feb. 1), part of a select club that includes Clark Gable, Boris Yeltsen, Sherman Hemsley, Jill Kelly, Exene Cervenka, Rick James, and Langston Hughes. We have interesting meetings . . . .
OK, I've finally got an answer that I trust to Jerry O'Donnell's question: what's the probability that 36 randomly chosen months will fail to include at least 4 months. Approximately 0.0002149134772 (roughly 215 in a million).
With n=36, m=12, and k=4, we seek the probability that a randomly chosen function from an n-element set into an m-element set has a range of size at most m-k.
For a fixed r, the number of functions from an n-element set onto a fixed r-element set is well-known to be:
f(n,r)=sum((-1)^j*C(r,j)*(r-j)^n, j=0...r-1) where C(r,j) is the binomial coefficient.
Allowing the range to vary over all r-element subsets of the m-element set, the number of functions from an n-element set onto some r-element subset of the m-element set is given by:
g(n,r)=C(m,r)*f(n,r).
Allowing r to vary from 1 to m-k and dividing by the total number of functions from an n-element set to an r-element set gives a probability of:
sum(g(n,r), r=1...m-k)/m^n.
I evaluated this for the specific values of n, m, and k using both Excel and Maple. To get Maple to do it in a reasonable amount of time required rewriting the sum as:
sum((i/m)^n*sum(C(m,i+j)*C(i+j,i)*(-1)^j), j=0...m-k-i), i=1...m-k)
No. What the calculation shows is that what actually happened was very unlikely to have happened randomly. It provides evidence supporting your observation that the replies are not random. I think that's what the person who asked it was getting at.
Interestingly in the street I grew up in there were at least 3 of us who had that birthday - me, the kid next door and my friend's mum 2/3 houses away on the other side - what is the chance of that?
My dad's is 7 days later on the 10th.
I am also the first response with an October birthday.
Most science ignores what it can't measure, as science develops alongside methods of measurement. A lot of science concentrates on what you can do now. That is all the Kuhnian stuff of “normal science.” We have this, we can measure this, so we will carry on doing this for a bit longer. Eventually you have what Kuhn calls a paradigm shift when you can no longer ignore what your current methods don't measure and your data and your theories no longer work, or you keep finding data that doesn't fit the theory. But this is a slow process and not the day-to-day workings of science.
Birthdays!
Birthdays!
Mike Floorstand's discussion below prompted me to write this. There is, as he said, a probability of greater than 50% of two people sharing a birthday in a room of 23 people or more.
Well, there are lots more than 23 people on this site, so when are your birthdays?? Mine is January 11th.
# Posted on February 2nd 2009 by Joe CSS
Re: Birthdays!
June twenty-third (I was tempted to say February 31)
# Posted on February 2nd 2009 by fauxcelt
Re: Birthdays!
December 2nd
# Posted on February 2nd 2009 by tomw
Re: Birthdays!
august 25
# Posted on February 2nd 2009 by kk cats
Re: Birthdays!
December 20
# Posted on February 2nd 2009 by Fanning
Re: Birthdays!
july 11
# Posted on February 2nd 2009 by lisaniska
Re: Birthdays!
February 25, same as George Harrison and Enrico Caruso
# Posted on February 2nd 2009 by Greg the Piano Tuner
Re: Birthdays!
Greg the Piano Tuner... Snap!
# Posted on February 2nd 2009 by Jeremy
Re: Birthdays!
17th jan
same as Cassius Clay and Al Capone
# Posted on February 2nd 2009 by I ♥ Dow
Re: Birthdays!
Forget about George and Enrico, Greg. You've got JEREMY!
I have to make do with tomw. *sigh*. (Just kidding about "making do").
# Posted on February 2nd 2009 by oldstrings
Re: Birthdays!
30 September, same as the late Frankie Kennedy but a year earlier
# Posted on February 2nd 2009 by Hup
Re: Birthdays!
Thomas Jefferson and I, April 13th.
# Posted on February 2nd 2009 by SWFL Fiddler
Re: Birthdays!
January 21st.
# Posted on February 2nd 2009 by John Culhane
Re: Birthdays!
Dec 20...you and me, Fanning. Happy belated.
# Posted on February 2nd 2009 by irishfiddler32
Re: Birthdays!
May 12
# Posted on February 2nd 2009 by Jeremy Hughes
Re: Birthdays!
...so out of about 15 replies we already have three matches??
Weird...
# Posted on February 2nd 2009 by tomw
Re: Birthdays!
3rd of August, which I apparently share with Martin Sheen and Martha Stewart.
# Posted on February 2nd 2009 by Pat Mustard
Re: Birthdays!
Here's number 4 - I'm with you John C - Jan 21st
# Posted on February 2nd 2009 by Taminka
Re: Birthdays!
4 out of 17 born in January - interesting!
# Posted on February 2nd 2009 by Taminka
Re: Birthdays!
fanning / irishfiddler32: you're the same as my wife's bd.
Does that count? Maybe 50%
# Posted on February 2nd 2009 by Hup
Re: Birthdays!
April is the cruelest month. It leaps from bough to bough... 23rd of April
# Posted on February 2nd 2009 by Atahualpa Quigley
Re: Birthdays!
July 2.
# Posted on February 2nd 2009 by Jon Kiparsky
Re: Birthdays!
Missed it by that much |----|
July 3
# Posted on February 2nd 2009 by Reverend
Re: Birthdays!
Just turned 43, January 29th
# Posted on February 2nd 2009 by Fishmonger
Re: Birthdays!
Sept. 2nd. every bloomin' year!
# Posted on February 2nd 2009 by tctelboy
Re: Birthdays!
Last day of the fiscal year, and the day that all the coupons expire.
I teach statistics and probability, and last semester I offered to bet that there were at least two students in my class of 34 who shared a birthday. (There was around an 80% chance I'd be right.) My students, who apparently spend many weekends losing money at the local casino, all offered to take me up on the bet. They were so certain that they were right that they were willing to bet against their probability teacher. Not even the pair of twins in my class thought it unwise to bet against me. *sigh*
# Posted on February 2nd 2009 by Tall, Dark, and Mysterious
Re: Birthdays!
LOL! Just out of curiosity, were there any other shared birthdays besides the twins?
# Posted on February 2nd 2009 by Reverend
Re: Birthdays!
April 16th... Same as the pope, Charlie Chaplin, and Wilbur Wright!
Cheers,
Armand
# Posted on February 2nd 2009 by armandale
Re: Birthdays!
February 9th
# Posted on February 2nd 2009 by fiddleK
Re: Birthdays!
5th December
# Posted on February 2nd 2009 by davydd
Re: Birthdays!
House!
# Posted on February 2nd 2009 by ramblingpitchfork
Re: Birthdays!
May 3rd
# Posted on February 2nd 2009 by snorre
Re: Birthdays!
FiddleK, call it a match!
# Posted on February 2nd 2009 by Janek
Re: Birthdays!
August 31st, no match for me yet!
# Posted on February 2nd 2009 by camwebby
Re: Birthdays!
June 26th
# Posted on February 2nd 2009 by sashiko calico
Re: Birthdays!
May 21
# Posted on February 2nd 2009 by nigelg
Re: Birthdays!
Mine is august 30th, that's close, camwebby!
# Posted on February 2nd 2009 by Henk Bos
Re: Birthdays!
Isn't it statistically odd that, out of the first 36 replies, four complete months are totally unrepresented?
# Posted on February 2nd 2009 by Jerry O'Donnell
Re: Birthdays!
Whats the chance of two people with consecutive membership numbers having birthdays on consecutive days?
(From what I've seen on this site over the years I know there's someone out there who will rise to this challenge for us, so the rest of us can get on with our lives)
# Posted on February 2nd 2009 by showaddydadito
Re: Birthdays!
Gregorian Calendar?
# Posted on February 2nd 2009 by Krick Stahlschwanz
Re: Birthdays!
February 25 - snap, Jeremy and Greg!!!!!
# Posted on February 2nd 2009 by domhnall.
Re: Birthdays!
September 5, same as Jesse James and Jack Daniel
# Posted on February 2nd 2009 by Ramiro
Re: Birthdays!
"Whats the chance of two people with consecutive membership numbers having birthdays on consecutive days? "
Assuming you mean 'at least two....' the answer changes as membership grows (gets more likely). I think you have to do it by working out the chance that >=2 do NOT have the same birthday (then take that away from unity)
ie chance that member #2 is NOT on Feb 26 AND
chance that member #3 is not on day after #2 AND etc
is (364/365)^52846 ignoring leap years
ie VERY small (about 1.1*10^(-63) )
In fact you only need a membership of about 250 for you to have a 50:50 chance of consecutive members having consecutive birthdays
Anyway, nuff of that nonsense!
# Posted on February 2nd 2009 by domhnall.
Re: Birthdays!
November 4th
First November so far i think
# Posted on February 2nd 2009 by Joneser
Re: Birthdays!
In answer to Jerry O'Donnell's question: somewhat. The probability that 36 randomly chosen birthdays omit at least 4 months is approximately 1.6%. The chances of them omitting 4 specific months are about 32 out of a million.
In answer to showaddydadito: ignoring Feb 29 (which wouldn't change the answer by much), it's 1-(363/365)^(number of members). This number is something like .9999... with about 127 nines before it has a different digit.
# Posted on February 2nd 2009 by GaryAMartin
Re: Birthdays!
Thank you Gary and dom - I bet it would be you two who came up with answers.
I won enough to buy my lunch.
# Posted on February 2nd 2009 by showaddydadito
Re: Birthdays!
24th June
# Posted on February 2nd 2009 by jlocky
Re: Birthdays!
21st March
# Posted on February 2nd 2009 by dontshoutout
Re: Birthdays!
..but Gary, the 363/365 in your formula allows for the member with higher membership no. to have the "LOWER" birthday. Maybe that's ok, maybe not . (who cares?)
.and as for 32 out of 1000000, isn't it just (8/12)^36 for specified months? ie .45 out of 1m?
Anyway, I can see a stern email coming our way with instructions to do penance by now posting 10^6 ITM related comments/discussions
# Posted on February 2nd 2009 by domhnall.
Re: Birthdays!
Domnull - whoever sends that email had better copy it to everyone, including the guy who put the eighth post on this discussion - someone called Jeremy.
# Posted on February 2nd 2009 by showaddydadito
Re: Birthdays!
anyone's birthday today?
well 127 years ago James Joyce was born, author of one of the most controversial books ever written 'Ulysses' (1922) _ bit of an irish connection
to me, by way of further deviation the following musicians are :
84, Elaine Stritch, actor and singer
65, Sir Andrew Davis, conductor
51, David Newton, jazz pianist and composer
41, Simon Wickham-Smith, musician and astrologer
38, Michelle Gayle, singer and actor
to me, i go with Bernard Baruch's :
'To me, old age is always 15 years older than i am.'
# Posted on February 2nd 2009 by lisaniska
Re: Birthdays!
June 21. Longest day of the year, according to my mother.
# Posted on February 2nd 2009 by Bob himself
Re: Birthdays!
Close Joe, mines January 12th
Mary
# Posted on February 2nd 2009 by Antikhntr
Re: Birthdays!
Bob, that depends on which hemisphere you live on.
# Posted on February 2nd 2009 by Ramiro
Re: Birthdays!
I live mostly in the right hemisphere.
# Posted on February 2nd 2009 by Bob himself
Re: Birthdays!
Sorry for the delay, Domnull; had to get dressed, drive 20 miles, and teach two classes in the last 3 hours. Yes, the 363/365 is because the question didn't require the higher member number to have a later birthday, just to be consecutive.
(8/12)^36 is for omitting a specific 4 months. (But I screwed up and used 8/12=.75 instead of .666...!) Sorry.
Also, omitting any 4 months is quite a bit more likely than omitting 4 specific months. Still, I screwed that one up. I just did it as C(12,4)(8/12)^36 (with the same arithmetic error), when it should really be a complicated inclusion/exclusion formula.
# Posted on February 2nd 2009 by GaryAMartin
Re: Birthdays!
Glad that's sorted out
# Posted on February 2nd 2009 by domhnall.
Re: Birthdays!
April 3rd
# Posted on February 2nd 2009 by JosephC
Re: Birthdays!
Reverend - amazingly enough, aside from the twins, there was another pair of students with the same birthday (different years), and one student had the same birthday as me! Now THAT I wouldn't have bet on.
# Posted on February 2nd 2009 by Tall, Dark, and Mysterious
Re: Birthdays!
April 6th.
Same as Ian Paisley ( well, that proves astrology can't be right, just for a start ), Paul Daniels ( an annoying illusionist ), Andre Previn, and Rory Bremner.
# Posted on February 2nd 2009 by Guernsey Pete
Re: Birthdays!
Mine's May 23, but also wanted to note that today is James Joyce's birthday.
# Posted on February 2nd 2009 by GaryAMartin
Re: Birthdays!
March 23 - same as Doc Watson (and Joan Crawford)
# Posted on February 2nd 2009 by airport
Re: Birthdays!
Should I be glad that I am not the only member of The Session who was born in June?
# Posted on February 2nd 2009 by fauxcelt
Re: Birthdays!
April 10th same as er.. Steven Seagul actor
# Posted on February 2nd 2009 by upmine3
Re: Birthdays!
I really was born yesterday (Feb. 1), part of a select club that includes Clark Gable, Boris Yeltsen, Sherman Hemsley, Jill Kelly, Exene Cervenka, Rick James, and Langston Hughes. We have interesting meetings . . . .
# Posted on February 2nd 2009 by Jameson Stew
Re: Birthdays!
man, upmine, I wouldn't go calling him "Steven Seagul" to his face! LOL
# Posted on February 2nd 2009 by Reverend
Re: Birthdays!
May 6, same as Sigmund Freud and Tony Blair.
# Posted on February 3rd 2009 by DrSilverSpear
Re: Birthdays!
OK, I've finally got an answer that I trust to Jerry O'Donnell's question: what's the probability that 36 randomly chosen months will fail to include at least 4 months. Approximately 0.0002149134772 (roughly 215 in a million).
With n=36, m=12, and k=4, we seek the probability that a randomly chosen function from an n-element set into an m-element set has a range of size at most m-k.
For a fixed r, the number of functions from an n-element set onto a fixed r-element set is well-known to be:
f(n,r)=sum((-1)^j*C(r,j)*(r-j)^n, j=0...r-1) where C(r,j) is the binomial coefficient.
Allowing the range to vary over all r-element subsets of the m-element set, the number of functions from an n-element set onto some r-element subset of the m-element set is given by:
g(n,r)=C(m,r)*f(n,r).
Allowing r to vary from 1 to m-k and dividing by the total number of functions from an n-element set to an r-element set gives a probability of:
sum(g(n,r), r=1...m-k)/m^n.
I evaluated this for the specific values of n, m, and k using both Excel and Maple. To get Maple to do it in a reasonable amount of time required rewriting the sum as:
sum((i/m)^n*sum(C(m,i+j)*C(i+j,i)*(-1)^j), j=0...m-k-i), i=1...m-k)
Phew! Took me about 4 hours.
# Posted on February 3rd 2009 by GaryAMartin
Re: Birthdays!
You missed out the propensity for people to reply to this thread if they have already seen their birthday, or something close, mentioned.
# Posted on February 3rd 2009 by ...
Re: Birthdays!
I didn't actually miss it. I chose to ignore it because there's no way to account for it with the available information.
# Posted on February 3rd 2009 by GaryAMartin
Re: Birthdays!
not a very practical science then, if you merely ignore what you can't measure
# Posted on February 3rd 2009 by ...
Re: Birthdays!
No. What the calculation shows is that what actually happened was very unlikely to have happened randomly. It provides evidence supporting your observation that the replies are not random. I think that's what the person who asked it was getting at.
# Posted on February 3rd 2009 by GaryAMartin
Re: Birthdays!
October 3rd
Same as Chubby Checker, Gore Vidal and Tommy Lee.
Interestingly in the street I grew up in there were at least 3 of us who had that birthday - me, the kid next door and my friend's mum 2/3 houses away on the other side - what is the chance of that?
My dad's is 7 days later on the 10th.
I am also the first response with an October birthday.
# Posted on February 3rd 2009 by No Cause For Alarm
Re: Birthdays!
Most science ignores what it can't measure, as science develops alongside methods of measurement. A lot of science concentrates on what you can do now. That is all the Kuhnian stuff of “normal science.” We have this, we can measure this, so we will carry on doing this for a bit longer. Eventually you have what Kuhn calls a paradigm shift when you can no longer ignore what your current methods don't measure and your data and your theories no longer work, or you keep finding data that doesn't fit the theory. But this is a slow process and not the day-to-day workings of science.
# Posted on February 3rd 2009 by DrSilverSpear
Re: Birthdays!
March 18th
The day after St. Pad, the day before number 2 from The Prisoner.
Win win win.
# Posted on February 3rd 2009 by Jams_O'Donnell
Re: Birthdays!
anyone's birthday today? lisaniska
yes I am a 2-2 groundhog day bd
with James Joyce et al.
bd yesterday
# Posted on February 4th 2009 by dogmageek
Re: Birthdays!
Call me a cynic if you will, but I've noticed that no-one thus far has answered:
20th April (same as Adolf Hitler)
or: 21st December (same as Josef Stalin)
or: 29th July (same as Benito Mussolini)
# Posted on February 4th 2009 by Mix O'Lydian
Re: Birthdays!
Right- we've done date of birth- now, how about mother's maiden name?
# Posted on February 4th 2009 by Here Lyeth
Re: Birthdays!
Christy Moore is 64
# Posted on May 7th 2009 by lisaniska
Re: Birthdays!
Do we still need him? Will we still feed him?
# Posted on May 8th 2009 by sashiko calico