I remember reading (thought it was on SD) how to calculate the odds of two people having the same birthday. It ended up that if you had something like 25 people in a room the odds where that 2 of them would have the same birthday. A search of the archives turned up nothing. Can anbody point me to the location of such an explination?
thanks
It’s know as the birthday paradox. Google gives some sites:
Its actually quite simple. If there are two people, then the odds of them having the same birthday are 1/365. So the odds of them not having the same dirthday are 1 - 1/365 = 364/365. If a third guy comes in, the odds that he will have the same birthday as either one of these guys is 2/365. The odds that he will not are 1 - 2/365 = 363/365. So the odds that both the first two guys have different birthdays and the third has a different birthday are 364/365 * 363/365. Going down the line can get you odds on any number of people.
Here is another link from the Skeptical Inquirer on this exact topic.
Incidentally, there is a Milwaukee family who just had their 4[sup]th[/sup] generation with the same birthday.
The story gives the odds as 1 in 48 million, which can be calculated as (1/365)[sup]3[/sup]
I don’t think the Milwaukee family is that much of a coincidence. The odds the newspaper gives assumes the birth (and therefore the conception) dates are completely random, but let’s take a closer look…
They were all born in August, which means they were all conceived around the beginning of the long Wisconsin winter. Lots of time indoors and not a whole lot to do… the results seem pretty obvious :D. Unless the wife is already pregnant, the odds look pretty good that a child will be conceived during the first ovulation of winter, which lowers the chances of a quadruple birthday to around 28[sup]4[/sup] , or about 600,000 to 1. Admittedly still pretty long.
–sublight.
If the family has more than one generation living together,
and tends to have kids young, I’d argue that your base of
28 is even high. Synchronized ovulating and all.
I am skeptical of the previous two posts. But I don’t see significance of something with 1 in 48 million odds. Considering the number of people in the world, there must be numerous such cases. (The article says that the Guiness Book people will list it - strange).
If you look at the odds for that particular family having the same birthday, then they’re pretty long… But if you look at the odds that that would happen to some family, somewhere in the U. S., then it’s much more reasonable.
If you’re ever giving a statistics lecture, it’s a pretty effective demonstration to test this. Project a calendar on an overhead, or whatever, and then, starting at the front, cross off peoples’ birthdays one-by-one until you get a match. With any reasonably sized class, you’re bound to find one.
Well, in an uncrowded field, it’s the most memorable statistics lecture demostration I’ve ever seen.
I saw that family on Good Moron America and they said they INDUCED the labor for the newest kid. It was her due date and her previous kids were born ‘early’. So she considered this baby to be late and was having the birth induced on this day to keep the streak going.
The one in the Guiness Book of World Records has a family with four children all born on February 29th, which I think is significant.
I don’t think that having even 10 kids born in one family on some given day is that significant though. Not even counting the inducement of labor to make it fit, it can’t be that difficult to plan the births to within a week or two. “Honey, it’s December 25th…come into the bedroom and unwrap your present.” 9 months later, a baby. Imagine my shock.