My wife's brother and I share the same birthday. What are the chances stastically of that happening?

Question

I lived in the Florida Keys, met my now-wife on the telephone through business dealings when she lived in Calgary Canada, and I took a Greyhound bus to meet her for the first time. Her brother was leery of me, but lightened up when we discovered we shared the same birthday.

Is it even POSSIBLE to calculate the stastical probability of this kind of thing happening, calculating in the chance that someone from Calgary would be interested in coming to work for a non-profit in Key West, and the romance developing, and the birthday thing?

Answer 1

I also have the same thing happen in my family. I married a man and my b-day is is September and my housbands nephew married a woman and her birthday is the exact same day, but she is a few hours older then me. We have the same first name, last name and b-day. Totally from two different families.

Answer 2

Copied from here: http://www.sciencenews.org/pages/sn_arc98/11_21_98/mathland.htm


One simple example of a coincidence that often surprises people involves birthdays.

It's rather unlikely that you and I share the same birthday (month and date). The more people you pull into the group, however, the more likely it is that at least two people will have matching dates.

Ignoring the minor technicality of leap years, it's clear that in a group of 366 people, at least two must share a birthday. Yet it seems counterintuitive to many that only 23 people are needed in a group to have a 50-50 chance of at least one coincidental birthday.

To see why it takes just 23 people to reach even odds on sharing a birthday, you have to look at the probabilities. Assume that all 365 days have an equal chance of being a birthday. For a party of one, there is no possibility of a coincidence. So, the probability of that particular date being a unique birthday is 365/365. For a second person to have a birthday that doesn't match that of the first, he or she must be born on any one of the other 364 days of the year.

You obtain the probability of no match between the birthdays of two people by multiplying 365/365 times 364/365, which equals .9973. Hence, the probability of a match is 1 – .9973, or .0027, which is much less than 1 percent.

With two people, there are 363 unused birthdays. The probability that a third person has a birthday that differs from the other two distinct birthdays is 363/365. So, for three people, the chance of having no pair of matching birthdays is 365/365 x 364/365 x 363/365, or .9918.

As the number of people brought into the group increases, the chance of there being no match decreases. By the time the crowd numbers 23 people, the probability of no matching birthdays is .4927. Thus, the chance of at least one match within a group of 23 people is .5073, or slightly better than 50 percent.

The reason the number is as low as 23 is that you aren't looking for a specific match. It doesn't have to be two particular people or a given date. Any match involving any date or any two people is enough to create a coincidence. Indeed, there are 253 different pairings possible among 23 people, any of which could lead to a match.

Answer 3

Statistically it is 1 in 365.25

A perfect random sampling of 365 people would mean that there is one birthday on each day of the year. If you bought one more person into the group (or sample) of 365, then that 366th person would have to share a birthday with one of the original group. That means you have a statistical probability of one in 365 for any two people to share the same birthday.

However, there are 365.256366 days in a year, so the answer to your first question is 1 in 365.25.

Just because the people are from two different countries has nothing to do with it. Now to bring the non-profit work and the romance into the equation, it would be a bunch of statistical hocus pocus.

However, if you were to try the same statistics with say bears, your probability of two bears sharing the same birthday would be much higher than 1 in 365.25, because bears are all born in the spring, and humans are born more or less evenly distributed in the year.

Answer 4

Well, I think you need like 26 (edit: actually 23) random people in a room to have the chance be over 50% that you have the same birthday as them. That's all I can add to this.

Oops! Spoke to soon, I found this too!
http://en.wikipedia.org/wiki/Birthday_paradox

Answer 5

This has been figured out and you can probably find it on the web. I remember reading it and I was amzed that it does not take many people for this to happen, I think it was between 10 and maybe 30.

Answer 6

1/365