## New Year Coincidence, 2015

(Submitted by Skepticality listener  Mark Gouch relayed to The Odds Must Be Crazy by Barbara Drescher.)

Here is the article (includes video) by Barry Wolf, WKYC.

But how can we say this is unbelievable as they do in the article? Sorry, but I can’t help myself here…

The odds would be one out of 365 * 365 * 365, or about one out of 48.6 million births. With 7 billion people on the planet, odds are that this has probably happened about 143 times ( to living persons. many more to those in the past). So rare, fun, and interesting, but not unbelievable.

I believe it happened based on the evidence (their claim that it did, which is good enough).

Actually since everyone has to have a birthday, we can ignore the first birthday, that of the man or the woman. So the odds someone marries someone with the same birthday (date of the year) as them is 1/365.

Then the odds their baby has that same birthday would be 1/(365 * 365) or 1/133,225. So with ~7 billion people this probably happened 52,543 times to persons living on the planet now.

The error in the first calculation is that the date was selected first. That calculation is correct for any specific date, whether it is January 1st or July 4th, or March 15th, or July 22nd. Anyone with better knowlege of probability please correct me if any of the above is incorrect.

As often happens, things that seem unbelievable are quite believable and things that are believed without evidence are not believable.

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 246.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog.

Good job!

You are correct with both calculations. It depends on how you frame it. If you’re wondering the odds of two people with the birthday of January 1st marrying and having a baby on January 1st, then the first is correct, but as you pointed out, that’s not really what’s interesting.

The only thing I would add is that these calculations also assume some things that we know are not true, such as that births are uniformly distributed across the days of the year. Even if natural births were (they aren’t), we’d see fewer births on days like January 1st simply because the number of scheduled C-sections and inductions is lower because it’s a holiday. However, figuring those few things in requires data that probably isn’t available.

## Wrap Your Brain Around Monty Hall

Monty Hall

I have always been amused and intrigued by responses to “The Monty Hall Problem”, especially when I talk about it to audiences with a high concentration of engineers and mathematicians. If you are familiar with it, but you’ve always struggled with an unsettled feeling of “this can’t be right”, read further and let me know if my explanation of the solution helps to alleviate the discomfort. If you are not familiar, I guarantee you will give your brain a workout by reading on.

First posed to statisticians in 1975, “The Monty Hall Problem” is well-known among academics because it still sparks debate. Many seem to think that disagreements about its solution stem from issues in the clarity of the problem, but I contend that it really stems from human flaws in the way that we process information.

I often discuss this problem in statistics and cognitive psychology courses for several reasons. It is a great exercise in probability calculation and it can be used to teach basic mathematical modeling (and its purpose). An added benefit, since almost all of my students were psychology majors, is that it also illustrates a flaw in human cognition as well as a pattern of problem solving.  Even a knowledgeable statistician feels the need to run simulations to see the solution in action. Even then, fully grasping the mechanisms behind the answer often requires brute force cognition.

In general, human beings have a very difficult time wrapping their brains around concepts of probability. It is much like a visual illusion; we know that the lines are parallel/the circles are the same size/there is no motion, but we can’t make our brains process it in a way that represents that reality. It’s just not how our visual system works. I hypothesize that one of the reasons that probability is such a difficult field for most people is that it involves theory and models, which are distinct from observations and we must represent them differently in our minds to properly deal with them. Applications of probability often involve switching gears from the realm of models to data or vice versa and this is where I think most mathematicians get side-swiped in The Monty Hall Problem.

### The Poser

In essence, here’s the problem: