Happy birthday to me! Today is my 27th birthday, so I am 26 years old. Woot.
Apparently, I share a birthday with two coworkers, a child of a friend from church, and the great entertainers Donny Osmond and R. Stephen Taylor. That got me thinking about the rather remarkably high probability that two folks in any given set of people will share a birthday.
Obviously, the chance that you and I share a birthday is only 1 in 366 (including February 29). But if you and I don’t share, and we add a third person, the probability that he would share either of our birthdays is 2 in 366. The more folks we add, the better chance that two will share a birthday. If we have a group of 367, we are guaranteed that two will share a birthday. So, the probability that two of us will not share a birthday is expressed as follows:
P = (366/366) * (365/366) * (364/366) …
| # of people in a set | Chance that none of them will share a birthday | Chance that two people in that group will share a birthday |
| 15 | 74.77% | 25.23% |
| 23 | 49.37% | 50.63% |
| 32 | 24.76% | 75.24% |
| 41 | 9.75% | 90.25% |
| 57 | 1.00% | 99.00% |
Try this at the next boring party or business lunch: see if you can find two people who share a birthday. I’ve attached a spreadsheet that calculates the probability for any size group.
BTW, I will accept cash or check for my birthday; also, my Amazon wish list is fully stocked and prioritized for your convenience…
think hard, think well 