Neat coin flipping problem found on Twitter yesterday

An essay by Jeremy Kun, a graduate student at the University of Illinois at Chicago, published on Edsurge on Feb 12 caused quite a stir on twitter yesterday.  I’m not interested in getting drawn into the discussion about the essay, but if you haven’t see it, you can read it here:

https://www.edsurge.com/n/2014-02-12-opinion-you-never-did-math-in-high-school

One response that seemed to get a lot of traction is here:

http://christopherdanielson.wordpress.com/2014/02/13/edsurgemath/

I first saw a reference to the Edsurge piece in a tweet from Justin Lanier yesterday morning:

I didn’t know what Justin was referring to, so I checked out @mathprogramming’s blog and found a really neat problem about coin flipping.    That piece is here:

http://jeremykun.com/2014/02/08/simulating-a-fair-coin-with-a-biased-coin/

We had lots of free time yesterday because of the blizzard, so I turned the coin flipping article into a fun afternoon project with the boys.

First I walked them through the problem – if we have some coins that don’t flip heads/tails 50% of the time, how can we use these coins to make 50/50 decisions?  It is a pretty neat problem:

With that as the introduction, we moved to the whiteboard and discussed a little bit about probability.  Some of the details were a bit above what my kids have studied, but not so much that they were totally lost.  I was actually pretty happy to be able to talk through a problem that used fractions since I just finished up a unit on fractions with my younger son last week.  It is always nice when a new or advanced problem lets you sneak in a little review 🙂

Finally, having worked through the probabilities, we jumped over to the computer to write a little program to simulate the problem.  I like to use Khan Academy’s programming site with the kids because it is easy to share.  The code in the original blog entry is obviously more compact than mine (to say the least!), but I thought breaking the problem into a few different chunks would help them understand the code a little better.  The program is here if you want to play with it:

https://www.khanacademy.org/cs/coin-flipping/5632235388534784

and the discussion where I walk the boys through the code is here:

As I said above, I really liked this activity.  I think the problem will be really fun for any kids who’ve played around a little with fractions and percents and also for any kids looking to learn some basics of computer modelling.

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Comments

One Comment so far. Leave a comment below.
  1. Ted V,

    Great FamilyMath Mike! Kind of reminds me of an exercise in looking at tail events (95th to 99th percentiles) by sampling in the upper distributions. But yours is way easier to understand.

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