Quandaries and Queries

Name: Martin

Who is asking: Other
Level: All

My wife and I have a question about the probability of something that happened to us a few years ago. So far, no one has been able to give me even an approximate answer. On my 32nd birthday, my wife and I went out to eat at local Japanese hibachi style restaurant. At the restaurant, couples/families are sat together around the hibachi where the cook performs a show. There was a fifteen minute or so wait, so my wife and I sat in the lounge waiting for our name to be called. When they called our names for the reservation, this is what happened. The first group called was the Martin family. Then they called the Francis family. We were the next family to be called, the Ashton family. My full name is Martin Francis Ashton! I think the odds of that happening to someone are very unlikely, but it did, and there is more. Next, we were all sat at the same table in that order, "Martin" family, "Francis" family, then us, the "Ashton" family. Again, it formed my full name!

After we all were seated, and started talking about the coincidence of that happening, I soon discovered that myself, and a male member of each of the other two families were celebrating their birthday, which is December 28th. All of us were celebrating one day late, December 29th, and all three of us were born ten years apart. 1959 for the man in the Martin family, 1979 for the man in the Francis family, and 1969 for myself, the Ashton family. That was the only thing that did not fall in order like my name did, and the fact that we were all celebrating a day late. Also, as a side note, none of us were born or raised in the city we all now live in, San Diego, California, and all three families moved here in 1999. Which adds to the improbability of it all. I wish I had thought to ask what month/day they had moved here, and where they came from, but I did not. I couldn't imagine the odds if they had moved here on the same month/day, and had came from the same city I had! But I digress.

I apologize that this is such a long email, but I wanted to give as many details as possible for any equation you might be able to come up with for this. No one I have talked to has a clue as too what the probability of that happening. Nor does anyone I know even know what it would take to make an equation to figure it out. Also, some people we tell the story to says it is too improbable, and could not have really happened even though it did. My family and I have been itching our heads about this one for two years, and really want to know the odds of what happened, and the odds that it would ever happen again. I do appreciate the time you have taken to read this email, and would greatly appreciate it if you could solve this mystery for us. Thank you.

Martin Francis Ashton
(I swear it really happened!!!)

Hi Martin,

Trillions of events happen every day. People walk down the street and contact other people, they go to restaurants, ride on busses,... . Some of these events seem unusual. You sit beside someone on the bus whose wife has the same name as yours. You probably don't know about this since you don't usually have long conversations with people you meet by chance.

The three families that you mention, the "Martin" family, the "Francis" family, and the "Ashton" family could have been seated next to each other in a theatre. Again you probably wouldn't be aware of this. What I see as fascinating about what you describe is that this was a situation where you became aware of the "unusualness" of the occurrence.

What is the probability of such an unusual event happening? I would say it is 1, that is it is certain to happen.

This may seem counter intuitive, but some probabilities defy our intuition. If you ask a random collection of 50 people, "On what day of the year is your birthday?" what is the probability the at least two of them reply with the same day? The probability is 0.97. It is virtually certain that at least two of them have the same birthday.


Go to Math Central