The Statistician's Twilight Zone

So, the other night, Cindi and I were watching a movie, and Cindi brought 6 dark chocolate Dove miniatures for each of us. You know, the kind that have foil wrappers like this...


... with touchy feely messages. I opened my first, and the message was "Make a list of your dreams." My second had the same message. My third said "Naughty can be nice." So did my fourth. That was starting to weird me out. I opened my fifth, and it said "Send a love letter this week." We joked that my sixth would say the same thing. Ha ha ha.

So I opened my sixth, and it said "Send a love letter this week." (weird music starts playing in my head).


For a statistician, I was feeling like a very special outlier, or in distributional terms, I was living in the twilight zone of extremely rare occurrences. Just to put this in perspective, here are a few calculations on the probability of the occurrence based on the assumption that there are 15 different messages and that sampling with replacement is the best mathematical representation of reality:

* Draw 1, probability of choosing any of the 15 messages = 15/15
* Draw 2, probability of choosing the message in draw 1 = 1/15
* Draw 3, probability of choosing a different message = 14/15
* Draw 4, probability of choosing the message in draw 3 = 1/15
* Draw 5, probability of choosing a message not yet seen = 13/15
* Draw 6, probability of choosing the message in draw 5 = 1/15

Multiply all of these individual probabilities together, and you get

0.024% = 0.00024 = 3/12,500

Whoa doggie, and knock me down with a feather!

I could do other calculations that would identify the likelihood that Dove would put a certain mix of chocolates into the bag, and then that Cindi would pull out twelve chocolates of a certain mix, and that she would choose six for me that have the three messages twice repeated, and that I would select them in a certain order. Things would get really infinitesimal then, but I would have to make even stronger assumptions.

Only a statistician, or as they say in the psychometric world, only the office psycho...