Problem #5 from Mosteller’s 50 Challenging Problems in Probability

Today we tackled our 5th problem from Mosteller’s 50 Challenging problems in probability. The proble involves geometric probability and asks about tossing a coin onto a grid.

Here’s how I introduced the problem to the kids. My younger son identified the task that we needed to do pretty quickly -> find a region in a single square that will help us describe when we win or lose the game.

Now that we had an idea of the geometric problem that we needed to solve, we tried to solve that problem. Although the boys were able to describe the winning region, it was very hard for them to move beyond that description:

We kept trying to describe the shape and focus on the important properties of that shape. In this video my older son was drawing a shape that I thought would get him to the main idea – but I was not interpreting his drawing the right way.

At the end of the last video the boys thought that focusing on the center of the circle would be a good way to go. Here they drew a picture of how the center moved and then tried to describe some properties of that square:

In the last video the boys came to the conclusion that if the center of the coin landed in a particular square we would win the game and if it landed outside of that square we would lose the game.

With that information, we found our probability of winning and then calculated if this is a game we should play.

[sorry that I forgot to zoom out until near the end of this video]