(Submitted by Skepticality listener Katharine Shade)

Today during my 7 year old’s violin lesson, I was reading a “Mr. Men” book to my 4 year old. He had selected it randomly from the teacher’s complete set of the books.

I had just finished a page which mentioned “Mrs. Twinkle”, when my daughter started playing “Twinkle Twinkle Little Star”.

It wasn’t as a direct result of my reading – she was working her way backwards through her repertoire of pieces, so that had been set in motion before I’d even started reading the book. And there was nothing to specifically draw my son to this book.

I often notice that I’m reading a word at about the same time I hear somebody say it, but that easily make sense considering the number of words I read. But my daughter only knows about 6 violin pieces by heart!

So what are the odds?

Below are the extended notes provided by mathematician Brian Pasko for use in Skepticality Episode 267.  Brian is on the faculty at a university in the southwestern United States. His interests include scientific skepticism, popular science books and improbable coincidences that makes one wonder just what the fates are up to. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

What a lovely vision: a young mother dramatically reading to the toddler in her lap while her daughter struggles through the elementary musical cannon. I can only hope that afternoon sunlight was streaming through the large windows of the studio…

How probable was your experience? I would say rather high! Of course, what questions we ask determines our estimate of the probability. Let’s start this way: the probability that a children’s book contains the word twinkle, fairly high; the probability that at some point during the lesson your seven year old daughter plays Twinkle, Twinkle Little Star I would say pretty close to one. (Probability is measured between zero and one with zero being cannot happen and one being cannot not happen.) In this case your experience is not that hard to believe.

Or, we could wonder what the probability is of reading a book with a character Miss Spider, Mr. Farmer, Ms. Wheels or, Madame Spaghetti (atop or otherwise) and noticing that your daughter plays one of the corresponding songs. In this case, your coincidence is even expected.

We can be a bit more specific, though we have to make some assumptions. There are numerous titles in the Mr. Men series but a box set of 50 books was issued in 2010, let’s suppose your son picked the book you read from one of these. I have been unable to determine the number of these books that include the character Mrs. Twinkle but let’s just assume two. (Yes, a bit arbitrary but it seems unlikely that she appears in only one title; if she is a regular character in the series, I expect a Google search would turn up some mention of her.) Twinkle, Twinkle Little Star takes about 30 seconds to play. Reading a Mr. Men book takes about 10 minutes and if the words ‘Mrs. Twinkle’ appears on three pages there is a 2 minute window that you could read the words ‘Mrs. Twinkle’ while your daughter is playing the song.

I wrote a short computer program to model the situation assuming the lesson was thirty minutes long. It turns out that the probability that you read the words “Mrs. Twinkle” while your daughter was playing Twinkle, Twinkle Little Star is about 0.27. Since two of the 50 books your son could have chosen include this character, I estimate the probability of your experience around 1.1%.

So, I think your improbable event is not all that improbable. Imagine the alternative: that one chooses a children’s book that does not have some similarity to a common children’s song.