Birthday Coincidence

This past weekend some friends and I visited Vancouver, B.C. We arrived around 8pm Friday night at our couch surfing host just a few minutes from downtown Vancouver. We went to dinner at India Bistro on Davie St. and started chatting.

Dave, our host, was in his 20s. I forgot what subject the conversation was on, but at one point, Dave mentioned that his parents bought their house in 1983. Earlier he had mentioned being born after they bought it, so I said, "Oh, you were born in 1984? What month?"

Dave said, "August."

I continued, "What day?"

He replied, "The 16th."

Immediately I whipped out my wallet to show him my driver's license, which proved to him that my birthday is also August 16, 1984.

CRAZY COINCIDENCE. Considering that Vicki, my twin, was there as well, there were three of us at the table of six sharing the exact same birthday.

I've heard of the "birthday paradox," how statistically, the probability of sharing a birthday with someone in a room of 23 is actually pretty high: 50%. But that's just sharing the same date, not both the date and year. And the reason it's so high is because it's the probability that ANYONE would share a birthday with ANYONE ELSE in the room. It considers that EACH of the 23 people may share a birthday with THE OTHER 22, so that's a lot of different pairs of people being considered. (In a group of 23 people there are 23×22/2 = 253 pairs.)

In this case, I'm only considering myself paired with Dave. I already know that I don't share a birthday with anyone in our travel party other than Vicki, so Dave is the only person the calculation applies to, so just one pair, rather than 253, which drastically limits the odds.

The odds of having the same birthday as anyone are 1/366 (counting the extra day of a leap year). Knowing that Dave was in his 20s, the odds of sharing the same birthyear are 1/10. So the odds of sharing both a birthday and birthyear with any 20-something in the world, randomly, are 1/3660.

Crazy.