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Sekhar Ramakrishnan writes:

I wanted to relate an episode of informal probabilistic reasoning that occurred this morning, which I thought you might find entertaining.

Jan 6th is the Christian feast day of the Epiphany, which is known as Dreikönigstag (Three Kings’ Day), here in Zürich, Switzerland, where I live (I work at ETH). There is a tradition to have a dish called three kings’ cake in which a plastic king is hidden in one of the pieces of the cake. Whoever finds the king gets some privileges that day (like deciding what’s for dinner).

Two years ago, the bakery we get our three kings’ cake from decided to put a king in *every* piece of cake. They received many complaints about this, and last year they returned to the normal tradition of one king per cake. Today, we were speculating on whether they were going to try their every-piece-a-king experiment again this year.

My 12-year-old son picked the first piece of cake: he had a king! He said, “It looks like they probably did put a king in every piece again this year.” We had a cake with 5 pieces, so, assuming that one king per cake and five kings per cake are equally likely, I get a posterior probability of 5/6 that there was a king in every piece. I thought it was interesting that my son intuitively concluded that a king in every piece was more likely as well, even though he hasn’t had any formal exposure to statistics or statistical reasoning.

As it turns out, though, there was only one king in the cake — my son just got lucky!

Indeed, there are some settings where probabilistic reasoning is intuitive.