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Ask Marilyn: The Birthday Paradox Party
Carl Gumbiner of Omaha, Nebraska, writes:
Marilyn: I want to share an amazing story. Recently, I was at a social event (a scotch-tasting). In the course of conversation, I made a bet with my friend Alan that there were two people at the tasting that shared the same birthday. I hadn't counted the number of people scattered around the house, but I thought there were more than two dozen attendees, so I figured my bet was pretty close to even odds.
The challenge was learning everyone's birthday. I got my chance just before lunch when we all gathered to cut the traditional haggis. After the ceremony, when we were still in a sort of circle, I asked for everyone's attention. I described the bet, asking if everyone would state his or her birthday. Alan was about 20th to state his own birthday: October 19th. We continued the process around the room, with my hopes for winning rapidly waning. Finally, the last person in the room—a friend, Joe—told the rest of us that his birthday was...yes, you guessed it...October 19th. At first, Alan didn't believe him, but Joe produced his driver's license as proof.
It's not so surprising that I won the bet, but the fact that it was Alan's own birthday that was duplicated, and by the very last person in the room, left me wishing I could go out to a horse track and get a bet down on a trifecta.
Yes, you trumped the birthday paradox nicely! Readers, the so-called birthday paradox (not an actual paradox, but surprising, nonetheless) is that when 23 or more people are in a gathering, the chances are just over 50 percent that at least two of them will share a birthday. It's easy to prove, but hard to believe.
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