Too Random, Or Not Random Enough: Student Misunderstandings About Probability In Coin Flipping

A related reasoning prompt for probability. Is this possible? Why or why not?

On the one hand, simple experiments like dice rolling, coin flipping, and spinning spinners are very much overdone in elementary curricula around the world. On the other hand, they can be a way to experience and understand some truly massive ideas about chance.

Here is a lesson idea for coin flipping. I also wrote about this in my book, Teaching Mathematics Through Problem-Solving in K-12 Classrooms.

A coin flip is a true 50/50 proposition. It is, by definition, a fair game. We experience “50/50ness” as true randomness. If I flip a coin in front of you, and it lands heads, there is a decent chance that, if asked, you would predict that the next one would be tails.

So the idea for this lesson is this:

we think events are more random than they actually are.

Or put another way:

even in a probability experiment with just two outcomes, you will likely see longer streaks or strings of one outcome, given enough trials.

So here is the lesson idea:

1. Have students make a fake simulation of a 100 coin flip experiment. They should produce on paper something that looks like this:

HTHTHTHTHHTTTHHHTTHTHTHTHTHTHHHHTTTHTHTHHTTTHTHHTT