(Submitted by reader Bob LeDrew)

When I was a kid, I was at home one evening and the phone rang. I picked it up and said, “hello?”

“Hi! Is that Bob?”
“Yes.”
“Put your mother on the phone.”
“Can I tell her who’s calling?”
“Oh come on, Bob, stop messing around and put Evelyn on the phone.”

My mom’s name IS Evelyn. But I didn’t know the voice, and started to get a little creeped out by the presumption. We went back and forth, each of us getting irritated.

“Are you sure you’ve dialed the right number?”
“Is this 736-xxxx?”
“Yes.”
“Then put Evelyn on!”

I was flummoxed. This person wouldn’t say who they were. I didn’t recognize their voice. But they knew my name, my mother’s name, and had the right phone number?!

Somewhere in my brain, something made me ask “What area code did you dial?”
“702.”

?!!?!?!

We were in 902, the area code, for Nova Scotia, Canada. 702 is Las Vegas.

I explained this to the person on the other end of the line. She hung up, and I ran to tell my parents that somewhere in Nevada, there was someone with our phone number named Evelyn who had a son named Bob. CRAZY!

So, let’s start with the not-so-unusual: I am not surprised at all that there is a common name in the submitted story and my own, since “Bob” is so common that it is used like “Joe” to imply a typical man. According to babycenter.com, “Robert” was the #1 name for baby boys for decades, was among the top 10 until 1990, and has not left the top 100 in more than a century. But let’s look at the probabilities within the original story itself.

The odds of two households having a mother and son with identical names and phone numbers which differ by a single digit depend on the commonality of the names and available phone numbers. With just a little bit more information, namely the year in which this occurred, and a LOT of research and computation, we could estimate this fairly accurately. Without that information, we can still make a few assumptions and cut a few corners to determine if the odds are indeed as crazy as they seem. Keep in mind that as I write this I do not know the identity of the story’s author and I will limit the source of some estimates to information about the U.S. for practical reasons, even though part of the story involves Canada (which complicates matters, but should not affect the outcome tremendously).

First we’ve established that “Bob” is extremely common, regardless of the ages of the mother and son. “Evelyn” has not been in the top 10 since 1915, but it was in the top 100 until 1953, then dropped in popularity somewhat until 2008, when it returned to the top 100.

If we assume the mother in this story was born when her names were rather popular, but recent enough for this to happen after area codes were in use, I will guess that this occurred in the 1980s. If 3 in 1000 (averaging and rounding) of the women in this age group are named Evelyn and 25 in 1000 boys 8-18 years old were named Robert, then the probability of a mother and son having the names Bob and Evelyn as opposed to any other configuration are approximately 15:100,000 or 3 in 40,000. Not extraordinarily low given that, according to infoplease.com, there were more than 62 million family households in the U.S. in 1985, so more than 4600 of them probably had mother/son combinations who answered to Bob and Evelyn. Less than 10% of households in 1985 did not have phones, so let’s say that there were 4200 Bob/Evelyns who could receive the call.

Where this gets much trickier is in estimating the probabilities related to the phone numbers. There were limits to the possible phone numbers at the time, making a calculation of the probability that two mother/son combinations named “Bob and Evelyn” would have numbers one digit apart a lot more work than I am willing to do for fun. However, we can get close to this by estimating the probability that someone would reach such a couple by dialing a 10-digit number incorrectly. In this case, what is more relevant than those limitations is the number of active phone lines. Tradingeconomics.com estimates the number of fixed and mobile telephone lines in the U.S. in 1985 at over 116 million. With 4200 of those including a Bob/Evelyn, that’s more than 1 in 25,000.

If you only dial one number incorrectly, the number of ways to dial 10 digits incorrectly is 100, but depending on which number you dialed incorrectly, the odds of reaching a person are actually small given that fewer than 1 in 50 of the possible combinations of 10 digits was in use at the time.

So, let’s assume (again, conservatively), that 2 of the numbers you could dial incorrectly would reached an actual phone. The odds, then, of reaching one of the 4200 Bob/Evelyns by dialing a single number incorrectly are about 7 in one million.