What are the odds on sharing of birthdays?
My wife has the same birthday as her sister. This is not so surprising – they’re twins! Next door but one to me, the little boy has the same birthday as me – but that’s just a coincidence.
So, let’s have some fun. How many people do you need to get together to have a greater chance than not that two people in this gathering have the same birthday? Think about it and when you’re ready …
The answer is 23.
Surprised?
You’ll find the mathematical proof here.
March 24th, 2007 at 2:49 pm
The first time I saw this problem I remember being surprised that the answer was so small! It seems counter-intuitive; 23 is much less than 365.
An intuitive way to understand why the answer should be so small is to note that the significant factor is not so much the number of people in the gathering, but the number of pairs of people. Each pair represents a chance for a shared birthday.
What is the number of pairs among 23 people? Each person can be paired with any of 22 others, so that gives us 23 × 22. But then we’re counting each pair twice (A paired with B is the same as B paired with A), so we must divide by 2 to get the actual number of pairs: 23 × 22 / 2 = 253.
Now, 253 is not so small compared with 365, and the result is no longer so surprising!
March 26th, 2007 at 9:50 pm
We have some friends who share our wedding anniversary AND the wife shares a birthday with me. Surely the odds of that are a bit longer?
June 22nd, 2007 at 2:55 am
I have the same birthday as my daughter. My husband insists that the odds of that happening are 1 in 365.
Is that accurate?
June 23rd, 2007 at 11:19 am
Sounds right, Christine.