Stumbling through problem #4 in Mosteller’s 50 Challenging Problems in Probability

Sometimes I think a project is going to go really smoothly and I’m just plain wrong. Today was one of those days, unfortunately, as I completely misjudged how difficult this problem would be for my younger son.

He and I ended up spending another 20 min on the problem after the project was over and that time was much more productive. I’m kicking myself a little – and wish that I’d approached the problem differently – but you can’t win them all 🙂

With that disclaimer out of the way, problem #4 from Mosteller’s probability book is a classic:

How many rolls, on average, does it take to roll a 6 on a fair, 6-sided die?

Here’s the introduction to the problem and the initial thoughts from both kids:

Next I had the boys roll dice off camera and record how long it tool to roll a 6. Here are the results of those experiments:

Now we moved from experiments to diving into the math – this is where I probably should have realized that my younger son was struggling a bit to see the math, but I failed to see his struggle:

And then we get lost, unfortunately. I turn the camera off around 6 min and we spent 10 more min talk about the problem off camera. I share this video only so that I can go back and learn from it later and see what I could have done better. Not everything goes well all the time . . . .

While we spoke off camera my older son found a very clever way to solve the problem. Here he explains that solution and my younger son was able to chime in on one little mistake at the end. It was a nice silver lining to a project that went off the rails a little bit: